diff --git a/doc/whatsnew/fragments/10652.false_positive b/doc/whatsnew/fragments/10652.false_positive
new file mode 100644
index 0000000000..a5a7319a26
--- /dev/null
+++ b/doc/whatsnew/fragments/10652.false_positive
@@ -0,0 +1,3 @@
+Fix false positive for ``invalid-name`` on a partially uninferable module-level constant.
+
+Closes #10652
diff --git a/pylint/checkers/base/name_checker/checker.py b/pylint/checkers/base/name_checker/checker.py
index c2f2655282..3cb1c336da 100644
--- a/pylint/checkers/base/name_checker/checker.py
+++ b/pylint/checkers/base/name_checker/checker.py
@@ -520,9 +520,14 @@ def visit_assignname(  # pylint: disable=too-many-branches,too-many-statements
                         self._check_name("const", node.name, node)
                 else:
                     node_type = "variable"
+                    iattrs = tuple(node.frame().igetattr(node.name))
                     if (
-                        (iattrs := tuple(node.frame().igetattr(node.name)))
-                        and util.Uninferable not in iattrs
+                        util.Uninferable in iattrs
+                        and self._name_regexps["const"].match(node.name) is not None
+                    ):
+                        return
+                    if (
+                        util.Uninferable not in iattrs
                         and len(iattrs) > 1
                         and all(
                             astroid.are_exclusive(*combo)
diff --git a/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py b/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
index 9012cea417..9eae16b7c1 100644
--- a/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
+++ b/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
@@ -1,5 +1,5 @@
 """Tests for invalid name for names declared at module level"""
-# pylint: disable=missing-class-docstring, too-few-public-methods, missing-function-docstring
+# pylint: disable=missing-class-docstring, too-few-public-methods, missing-function-docstring, wrong-import-position
 
 import collections
 
@@ -42,3 +42,12 @@ def A():  # [invalid-name]
     other_const = [2]
 else:
     other_const = [3]
+
+
+from importlib.metadata import PackageNotFoundError
+from importlib.metadata import version
+
+try:
+    VERSION = version("ty")  # uninferable
+except PackageNotFoundError:
+    VERSION = "0.0.0"