diff --git a/doc/user_guide/checkers/extensions.rst b/doc/user_guide/checkers/extensions.rst
index 0e28d1d579..ec973dac07 100644
--- a/doc/user_guide/checkers/extensions.rst
+++ b/doc/user_guide/checkers/extensions.rst
@@ -110,7 +110,7 @@ Verbatim name of the checker is ``compare-to-zero``.
 
 Compare-To-Zero checker Messages
 ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-:compare-to-zero (C2001): *Avoid comparisons to zero*
+:compare-to-zero (C2001): *"%s" can be simplified to "%s" as 0 is falsey*
   Used when Pylint detects comparison to a 0 constant.
 
 
diff --git a/pylint/extensions/comparetozero.py b/pylint/extensions/comparetozero.py
index f418c1833b..116bf229a3 100644
--- a/pylint/extensions/comparetozero.py
+++ b/pylint/extensions/comparetozero.py
@@ -21,7 +21,11 @@
 
 
 def _is_constant_zero(node: str | nodes.NodeNG) -> bool:
-    return isinstance(node, astroid.Const) and node.value == 0
+    # We have to check that node.value is not False because node.value == 0 is True
+    # when node.value is False
+    return (
+        isinstance(node, astroid.Const) and node.value == 0 and node.value is not False
+    )
 
 
 class CompareToZeroChecker(checkers.BaseChecker):
@@ -36,7 +40,7 @@ class CompareToZeroChecker(checkers.BaseChecker):
     name = "compare-to-zero"
     msgs = {
         "C2001": (
-            "Avoid comparisons to zero",
+            '"%s" can be simplified to "%s" as 0 is falsey',
             "compare-to-zero",
             "Used when Pylint detects comparison to a 0 constant.",
         )
@@ -66,12 +70,25 @@ def visit_compare(self, node: nodes.Compare) -> None:
             # 0 ?? X
             if _is_constant_zero(op_1) and op_2 in _operators:
                 error_detected = True
+                op = op_3
             # X ?? 0
             elif op_2 in _operators and _is_constant_zero(op_3):
                 error_detected = True
+                op = op_1
 
             if error_detected:
-                self.add_message("compare-to-zero", node=node, confidence=HIGH)
+                original = f"{op_1.as_string()} {op_2} {op_3.as_string()}"
+                suggestion = (
+                    op.as_string()
+                    if op_2 in {"!=", "is not"}
+                    else f"not {op.as_string()}"
+                )
+                self.add_message(
+                    "compare-to-zero",
+                    args=(original, suggestion),
+                    node=node,
+                    confidence=HIGH,
+                )
 
 
 def register(linter: PyLinter) -> None:
diff --git a/tests/functional/ext/comparetozero/comparetozero.py b/tests/functional/ext/comparetozero/compare_to_zero.py
similarity index 51%
rename from tests/functional/ext/comparetozero/comparetozero.py
rename to tests/functional/ext/comparetozero/compare_to_zero.py
index 29fd13994a..6a14b8bc95 100644
--- a/tests/functional/ext/comparetozero/comparetozero.py
+++ b/tests/functional/ext/comparetozero/compare_to_zero.py
@@ -1,4 +1,4 @@
-# pylint: disable=literal-comparison,missing-docstring
+# pylint: disable=literal-comparison,missing-docstring, singleton-comparison
 
 X = 123
 Y = len('test')
@@ -6,15 +6,33 @@
 if X is 0:  # [compare-to-zero]
     pass
 
+if X is False:
+    pass
+
 if Y is not 0:  # [compare-to-zero]
     pass
 
+if Y is not False:
+    pass
+
 if X == 0:  # [compare-to-zero]
     pass
 
+if X == False:
+    pass
+
+if 0 == Y:  # [compare-to-zero]
+    pass
+
 if Y != 0:  # [compare-to-zero]
     pass
 
+if 0 != X:  # [compare-to-zero]
+    pass
+
+if Y != False:
+    pass
+
 if X > 0:
     pass
 
diff --git a/tests/functional/ext/comparetozero/comparetozero.rc b/tests/functional/ext/comparetozero/compare_to_zero.rc
similarity index 100%
rename from tests/functional/ext/comparetozero/comparetozero.rc
rename to tests/functional/ext/comparetozero/compare_to_zero.rc
diff --git a/tests/functional/ext/comparetozero/compare_to_zero.txt b/tests/functional/ext/comparetozero/compare_to_zero.txt
new file mode 100644
index 0000000000..a413a32682
--- /dev/null
+++ b/tests/functional/ext/comparetozero/compare_to_zero.txt
@@ -0,0 +1,6 @@
+compare-to-zero:6:3:6:9::"""X is 0"" can be simplified to ""not X"" as 0 is falsey":HIGH
+compare-to-zero:12:3:12:13::"""Y is not 0"" can be simplified to ""Y"" as 0 is falsey":HIGH
+compare-to-zero:18:3:18:9::"""X == 0"" can be simplified to ""not X"" as 0 is falsey":HIGH
+compare-to-zero:24:3:24:9::"""0 == Y"" can be simplified to ""not Y"" as 0 is falsey":HIGH
+compare-to-zero:27:3:27:9::"""Y != 0"" can be simplified to ""Y"" as 0 is falsey":HIGH
+compare-to-zero:30:3:30:9::"""0 != X"" can be simplified to ""X"" as 0 is falsey":HIGH
diff --git a/tests/functional/ext/comparetozero/comparetozero.txt b/tests/functional/ext/comparetozero/comparetozero.txt
deleted file mode 100644
index f29aabae50..0000000000
--- a/tests/functional/ext/comparetozero/comparetozero.txt
+++ /dev/null
@@ -1,4 +0,0 @@
-compare-to-zero:6:3:6:9::Avoid comparisons to zero:HIGH
-compare-to-zero:9:3:9:13::Avoid comparisons to zero:HIGH
-compare-to-zero:12:3:12:9::Avoid comparisons to zero:HIGH
-compare-to-zero:15:3:15:9::Avoid comparisons to zero:HIGH