diff --git a/doc/source/whatsnew/v2.2.0.rst b/doc/source/whatsnew/v2.2.0.rst
index 8209525721b98..89a03ddbef2a2 100644
--- a/doc/source/whatsnew/v2.2.0.rst
+++ b/doc/source/whatsnew/v2.2.0.rst
@@ -460,6 +460,7 @@ Other Deprecations
 - Deprecated behavior of :meth:`Index.insert` with an object-dtype index silently performing type inference on the result, explicitly call ``result.infer_objects(copy=False)`` for the old behavior instead (:issue:`51363`)
 - Deprecated casting non-datetimelike values (mainly strings) in :meth:`Series.isin` and :meth:`Index.isin` with ``datetime64``, ``timedelta64``, and :class:`PeriodDtype` dtypes (:issue:`53111`)
 - Deprecated downcasting behavior in :meth:`Series.where`, :meth:`DataFrame.where`, :meth:`Series.mask`, :meth:`DataFrame.mask`, :meth:`Series.clip`, :meth:`DataFrame.clip`; in a future version these will not infer object-dtype columns to non-object dtype, or all-round floats to integer dtype. Call ``result.infer_objects(copy=False)`` on the result for object inference, or explicitly cast floats to ints. To opt in to the future version, use ``pd.set_option("future.no_silent_downcasting", True)`` (:issue:`53656`)
+- Deprecated dtype inference in :class:`Index`, :class:`Series` and :class:`DataFrame` constructors when giving a pandas input, call ``.infer_objects`` on the input to keep the current behavior (:issue:`56012`)
 - Deprecated dtype inference when setting a :class:`Index` into a :class:`DataFrame`, cast explicitly instead (:issue:`56102`)
 - Deprecated including the groups in computations when using :meth:`.DataFrameGroupBy.apply` and :meth:`.DataFrameGroupBy.resample`; pass ``include_groups=False`` to exclude the groups (:issue:`7155`)
 - Deprecated indexing an :class:`Index`  with a boolean indexer of length zero (:issue:`55820`)
diff --git a/pandas/_testing/__init__.py b/pandas/_testing/__init__.py
index 69b2b0876fc80..672c16a85086c 100644
--- a/pandas/_testing/__init__.py
+++ b/pandas/_testing/__init__.py
@@ -10,6 +10,7 @@
     ContextManager,
     cast,
 )
+import warnings
 
 import numpy as np
 
@@ -285,11 +286,17 @@ def box_expected(expected, box_cls, transpose: bool = True):
         else:
             expected = pd.array(expected, copy=False)
     elif box_cls is Index:
-        expected = Index(expected)
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Dtype inference", category=FutureWarning)
+            expected = Index(expected)
     elif box_cls is Series:
-        expected = Series(expected)
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Dtype inference", category=FutureWarning)
+            expected = Series(expected)
     elif box_cls is DataFrame:
-        expected = Series(expected).to_frame()
+        with warnings.catch_warnings():
+            warnings.filterwarnings("ignore", "Dtype inference", category=FutureWarning)
+            expected = Series(expected).to_frame()
         if transpose:
             # for vector operations, we need a DataFrame to be a single-row,
             #  not a single-column, in order to operate against non-DataFrame
diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index e741fa7b37f33..e1048a51089ac 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -726,6 +726,10 @@ def __init__(
 
         manager = _get_option("mode.data_manager", silent=True)
 
+        is_pandas_object = isinstance(data, (Series, Index, ExtensionArray))
+        data_dtype = getattr(data, "dtype", None)
+        original_dtype = dtype
+
         # GH47215
         if isinstance(index, set):
             raise ValueError("index cannot be a set")
@@ -912,6 +916,18 @@ def __init__(
 
         NDFrame.__init__(self, mgr)
 
+        if original_dtype is None and is_pandas_object and data_dtype == np.object_:
+            if self.dtypes.iloc[0] != data_dtype:
+                warnings.warn(
+                    "Dtype inference on a pandas object "
+                    "(Series, Index, ExtensionArray) is deprecated. The DataFrame "
+                    "constructor will keep the original dtype in the future. "
+                    "Call `infer_objects` on the result to get the old "
+                    "behavior.",
+                    FutureWarning,
+                    stacklevel=2,
+                )
+
     # ----------------------------------------------------------------------
 
     def __dataframe__(
diff --git a/pandas/core/indexes/base.py b/pandas/core/indexes/base.py
index 5dc4a85ba9792..e01c4e75e9f8a 100644
--- a/pandas/core/indexes/base.py
+++ b/pandas/core/indexes/base.py
@@ -492,6 +492,8 @@ def __new__(
         if not copy and isinstance(data, (ABCSeries, Index)):
             refs = data._references
 
+        is_pandas_object = isinstance(data, (ABCSeries, Index, ExtensionArray))
+
         # range
         if isinstance(data, (range, RangeIndex)):
             result = RangeIndex(start=data, copy=copy, name=name)
@@ -571,7 +573,19 @@ def __new__(
         klass = cls._dtype_to_subclass(arr.dtype)
 
         arr = klass._ensure_array(arr, arr.dtype, copy=False)
-        return klass._simple_new(arr, name, refs=refs)
+        result = klass._simple_new(arr, name, refs=refs)
+        if dtype is None and is_pandas_object and data_dtype == np.object_:
+            if result.dtype != data_dtype:
+                warnings.warn(
+                    "Dtype inference on a pandas object "
+                    "(Series, Index, ExtensionArray) is deprecated. The Index "
+                    "constructor will keep the original dtype in the future. "
+                    "Call `infer_objects` on the result to get the old "
+                    "behavior.",
+                    FutureWarning,
+                    stacklevel=2,
+                )
+        return result  # type: ignore[return-value]
 
     @classmethod
     def _ensure_array(cls, data, dtype, copy: bool):
diff --git a/pandas/core/series.py b/pandas/core/series.py
index e4dca97bc645d..d46068b6338c5 100644
--- a/pandas/core/series.py
+++ b/pandas/core/series.py
@@ -424,6 +424,10 @@ def __init__(
                 self.name = name
             return
 
+        is_pandas_object = isinstance(data, (Series, Index, ExtensionArray))
+        data_dtype = getattr(data, "dtype", None)
+        original_dtype = dtype
+
         if isinstance(data, (ExtensionArray, np.ndarray)):
             if copy is not False and using_copy_on_write():
                 if dtype is None or astype_is_view(data.dtype, pandas_dtype(dtype)):
@@ -581,6 +585,17 @@ def __init__(
         self.name = name
         self._set_axis(0, index)
 
+        if original_dtype is None and is_pandas_object and data_dtype == np.object_:
+            if self.dtype != data_dtype:
+                warnings.warn(
+                    "Dtype inference on a pandas object "
+                    "(Series, Index, ExtensionArray) is deprecated. The Series "
+                    "constructor will keep the original dtype in the future. "
+                    "Call `infer_objects` on the result to get the old behavior.",
+                    FutureWarning,
+                    stacklevel=find_stack_level(),
+                )
+
     def _init_dict(
         self, data, index: Index | None = None, dtype: DtypeObj | None = None
     ):
diff --git a/pandas/core/strings/accessor.py b/pandas/core/strings/accessor.py
index 75866c6f6013a..1b7d632c0fa80 100644
--- a/pandas/core/strings/accessor.py
+++ b/pandas/core/strings/accessor.py
@@ -689,19 +689,18 @@ def cat(
             result = cat_safe(all_cols, sep)
 
         out: Index | Series
+        if isinstance(self._orig.dtype, CategoricalDtype):
+            # We need to infer the new categories.
+            dtype = self._orig.dtype.categories.dtype
+        else:
+            dtype = self._orig.dtype
         if isinstance(self._orig, ABCIndex):
             # add dtype for case that result is all-NA
-            dtype = None
             if isna(result).all():
-                dtype = object
+                dtype = object  # type: ignore[assignment]
 
             out = Index(result, dtype=dtype, name=self._orig.name)
         else:  # Series
-            if isinstance(self._orig.dtype, CategoricalDtype):
-                # We need to infer the new categories.
-                dtype = self._orig.dtype.categories.dtype  # type: ignore[assignment]
-            else:
-                dtype = self._orig.dtype
             res_ser = Series(
                 result, dtype=dtype, index=data.index, name=self._orig.name, copy=False
             )
diff --git a/pandas/tests/copy_view/test_constructors.py b/pandas/tests/copy_view/test_constructors.py
index 7d5c485958039..1aa458a625028 100644
--- a/pandas/tests/copy_view/test_constructors.py
+++ b/pandas/tests/copy_view/test_constructors.py
@@ -314,7 +314,8 @@ def test_dataframe_from_series_or_index_different_dtype(using_copy_on_write, con
 
 def test_dataframe_from_series_infer_datetime(using_copy_on_write):
     ser = Series([Timestamp("2019-12-31"), Timestamp("2020-12-31")], dtype=object)
-    df = DataFrame(ser)
+    with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+        df = DataFrame(ser)
     assert not np.shares_memory(get_array(ser), get_array(df, 0))
     if using_copy_on_write:
         assert df._mgr._has_no_reference(0)
diff --git a/pandas/tests/frame/test_constructors.py b/pandas/tests/frame/test_constructors.py
index e1abd0344e356..4c4760501db4e 100644
--- a/pandas/tests/frame/test_constructors.py
+++ b/pandas/tests/frame/test_constructors.py
@@ -2768,6 +2768,23 @@ def test_frame_string_inference_block_dim(self):
             df = DataFrame(np.array([["hello", "goodbye"], ["hello", "Hello"]]))
         assert df._mgr.blocks[0].ndim == 2
 
+    def test_inference_on_pandas_objects(self):
+        # GH#56012
+        idx = Index([Timestamp("2019-12-31")], dtype=object)
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            result = DataFrame(idx, columns=["a"])
+        assert result.dtypes.iloc[0] != np.object_
+        result = DataFrame({"a": idx})
+        assert result.dtypes.iloc[0] == np.object_
+
+        ser = Series([Timestamp("2019-12-31")], dtype=object)
+
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            result = DataFrame(ser, columns=["a"])
+        assert result.dtypes.iloc[0] != np.object_
+        result = DataFrame({"a": ser})
+        assert result.dtypes.iloc[0] == np.object_
+
 
 class TestDataFrameConstructorIndexInference:
     def test_frame_from_dict_of_series_overlapping_monthly_period_indexes(self):
diff --git a/pandas/tests/indexes/base_class/test_constructors.py b/pandas/tests/indexes/base_class/test_constructors.py
index 60abbfc441e8e..fd5176a28565e 100644
--- a/pandas/tests/indexes/base_class/test_constructors.py
+++ b/pandas/tests/indexes/base_class/test_constructors.py
@@ -5,6 +5,7 @@
 from pandas import (
     Index,
     MultiIndex,
+    Series,
 )
 import pandas._testing as tm
 
@@ -57,3 +58,16 @@ def test_index_string_inference(self):
         with pd.option_context("future.infer_string", True):
             ser = Index(["a", 1])
         tm.assert_index_equal(ser, expected)
+
+    def test_inference_on_pandas_objects(self):
+        # GH#56012
+        idx = Index([pd.Timestamp("2019-12-31")], dtype=object)
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            result = Index(idx)
+        assert result.dtype != np.object_
+
+        ser = Series([pd.Timestamp("2019-12-31")], dtype=object)
+
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            result = Index(ser)
+        assert result.dtype != np.object_
diff --git a/pandas/tests/indexes/test_base.py b/pandas/tests/indexes/test_base.py
index 185e34efdc177..666d92064c86c 100644
--- a/pandas/tests/indexes/test_base.py
+++ b/pandas/tests/indexes/test_base.py
@@ -104,7 +104,8 @@ def test_constructor_copy(self, index, using_infer_string):
     )
     def test_constructor_from_index_dtlike(self, cast_as_obj, index):
         if cast_as_obj:
-            result = Index(index.astype(object))
+            with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+                result = Index(index.astype(object))
         else:
             result = Index(index)
 
diff --git a/pandas/tests/series/accessors/test_dt_accessor.py b/pandas/tests/series/accessors/test_dt_accessor.py
index 083a4c4b24adb..34465a7c12c18 100644
--- a/pandas/tests/series/accessors/test_dt_accessor.py
+++ b/pandas/tests/series/accessors/test_dt_accessor.py
@@ -259,9 +259,9 @@ def test_dt_accessor_limited_display_api(self):
         tm.assert_almost_equal(results, sorted(set(ok_for_dt + ok_for_dt_methods)))
 
         # Period
-        ser = Series(
-            period_range("20130101", periods=5, freq="D", name="xxx").astype(object)
-        )
+        idx = period_range("20130101", periods=5, freq="D", name="xxx").astype(object)
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            ser = Series(idx)
         results = get_dir(ser)
         tm.assert_almost_equal(
             results, sorted(set(ok_for_period + ok_for_period_methods))
diff --git a/pandas/tests/series/methods/test_between.py b/pandas/tests/series/methods/test_between.py
index 8f4931beae589..3913419038876 100644
--- a/pandas/tests/series/methods/test_between.py
+++ b/pandas/tests/series/methods/test_between.py
@@ -20,7 +20,7 @@ def test_between(self):
         tm.assert_series_equal(result, expected)
 
     def test_between_datetime_object_dtype(self):
-        ser = Series(bdate_range("1/1/2000", periods=20).astype(object))
+        ser = Series(bdate_range("1/1/2000", periods=20), dtype=object)
         ser[::2] = np.nan
 
         result = ser[ser.between(ser[3], ser[17])]
diff --git a/pandas/tests/series/methods/test_equals.py b/pandas/tests/series/methods/test_equals.py
index b94723b7cbddf..875ffdd3fe851 100644
--- a/pandas/tests/series/methods/test_equals.py
+++ b/pandas/tests/series/methods/test_equals.py
@@ -82,13 +82,15 @@ def test_equals_matching_nas():
     left = Series([np.datetime64("NaT")], dtype=object)
     right = Series([np.datetime64("NaT")], dtype=object)
     assert left.equals(right)
-    assert Index(left).equals(Index(right))
+    with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+        assert Index(left).equals(Index(right))
     assert left.array.equals(right.array)
 
     left = Series([np.timedelta64("NaT")], dtype=object)
     right = Series([np.timedelta64("NaT")], dtype=object)
     assert left.equals(right)
-    assert Index(left).equals(Index(right))
+    with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+        assert Index(left).equals(Index(right))
     assert left.array.equals(right.array)
 
     left = Series([np.float64("NaN")], dtype=object)
diff --git a/pandas/tests/series/test_constructors.py b/pandas/tests/series/test_constructors.py
index 0e6f1c284a988..5f591b4b22f1c 100644
--- a/pandas/tests/series/test_constructors.py
+++ b/pandas/tests/series/test_constructors.py
@@ -1316,7 +1316,8 @@ def test_constructor_periodindex(self):
         pi = period_range("20130101", periods=5, freq="D")
         s = Series(pi)
         assert s.dtype == "Period[D]"
-        expected = Series(pi.astype(object))
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            expected = Series(pi.astype(object))
         tm.assert_series_equal(s, expected)
 
     def test_constructor_dict(self):
@@ -2137,6 +2138,20 @@ def test_series_string_inference_na_first(self):
             result = Series([pd.NA, "b"])
         tm.assert_series_equal(result, expected)
 
+    def test_inference_on_pandas_objects(self):
+        # GH#56012
+        ser = Series([Timestamp("2019-12-31")], dtype=object)
+        with tm.assert_produces_warning(None):
+            # This doesn't do inference
+            result = Series(ser)
+        assert result.dtype == np.object_
+
+        idx = Index([Timestamp("2019-12-31")], dtype=object)
+
+        with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+            result = Series(idx)
+        assert result.dtype != np.object_
+
 
 class TestSeriesConstructorIndexCoercion:
     def test_series_constructor_datetimelike_index_coercion(self):
diff --git a/pandas/tests/strings/test_cat.py b/pandas/tests/strings/test_cat.py
index 284932491a65e..c1e7ad6e02779 100644
--- a/pandas/tests/strings/test_cat.py
+++ b/pandas/tests/strings/test_cat.py
@@ -98,14 +98,18 @@ def test_str_cat_categorical(
 
     with option_context("future.infer_string", infer_string):
         s = Index(["a", "a", "b", "a"], dtype=dtype_caller)
-        s = s if box == Index else Series(s, index=s)
+        s = s if box == Index else Series(s, index=s, dtype=s.dtype)
         t = Index(["b", "a", "b", "c"], dtype=dtype_target)
 
-        expected = Index(["ab", "aa", "bb", "ac"])
+        expected = Index(
+            ["ab", "aa", "bb", "ac"], dtype=object if dtype_caller == "object" else None
+        )
         expected = (
             expected
             if box == Index
-            else Series(expected, index=Index(s, dtype=dtype_caller))
+            else Series(
+                expected, index=Index(s, dtype=dtype_caller), dtype=expected.dtype
+            )
         )
 
         # Series/Index with unaligned Index -> t.values
@@ -123,12 +127,19 @@ def test_str_cat_categorical(
 
         # Series/Index with Series having different Index
         t = Series(t.values, index=t.values)
-        expected = Index(["aa", "aa", "bb", "bb", "aa"])
+        expected = Index(
+            ["aa", "aa", "bb", "bb", "aa"],
+            dtype=object if dtype_caller == "object" else None,
+        )
         dtype = object if dtype_caller == "object" else s.dtype.categories.dtype
         expected = (
             expected
             if box == Index
-            else Series(expected, index=Index(expected.str[:1], dtype=dtype))
+            else Series(
+                expected,
+                index=Index(expected.str[:1], dtype=dtype),
+                dtype=expected.dtype,
+            )
         )
 
         result = s.str.cat(t, sep=sep)
diff --git a/pandas/tests/tseries/frequencies/test_inference.py b/pandas/tests/tseries/frequencies/test_inference.py
index 45741e852fef7..99a504f4188c1 100644
--- a/pandas/tests/tseries/frequencies/test_inference.py
+++ b/pandas/tests/tseries/frequencies/test_inference.py
@@ -23,6 +23,7 @@
     date_range,
     period_range,
 )
+import pandas._testing as tm
 from pandas.core.arrays import (
     DatetimeArray,
     TimedeltaArray,
@@ -206,7 +207,8 @@ def test_infer_freq_custom(base_delta_code_pair, constructor):
 )
 def test_infer_freq_index(freq, expected):
     rng = period_range("1959Q2", "2009Q3", freq=freq)
-    rng = Index(rng.to_timestamp("D", how="e").astype(object))
+    with tm.assert_produces_warning(FutureWarning, match="Dtype inference"):
+        rng = Index(rng.to_timestamp("D", how="e").astype(object))
 
     assert rng.inferred_freq == expected