diff --git a/Lib/annotationlib.py b/Lib/annotationlib.py
index bee019cd51591e..13590c62bee2d3 100644
--- a/Lib/annotationlib.py
+++ b/Lib/annotationlib.py
@@ -664,6 +664,17 @@ def call_annotate_function(annotate, format, *, owner=None, _is_evaluate=False):
         # possibly constants if the annotate function uses them directly). We then
         # convert each of those into a string to get an approximation of the
         # original source.
+
+        # Attempt to call with VALUE_WITH_FAKE_GLOBALS to check if it is implemented
+        # See: https://github.com/python/cpython/issues/138764
+        # Only fail on NotImplementedError
+        try:
+            annotate(Format.VALUE_WITH_FAKE_GLOBALS)
+        except NotImplementedError:
+            raise
+        except Exception:
+            pass
+
         globals = _StringifierDict({}, format=format)
         is_class = isinstance(owner, type)
         closure = _build_closure(
@@ -722,6 +733,10 @@ def call_annotate_function(annotate, format, *, owner=None, _is_evaluate=False):
         )
         try:
             result = func(Format.VALUE_WITH_FAKE_GLOBALS)
+        except NotImplementedError:
+            # If NotImplementedError is raised, don't try to call again with
+            # no globals.
+            raise
         except Exception:
             pass
         else:
diff --git a/Lib/test/test_annotationlib.py b/Lib/test/test_annotationlib.py
index 88e0d611647f28..5a2d8a558a2891 100644
--- a/Lib/test/test_annotationlib.py
+++ b/Lib/test/test_annotationlib.py
@@ -8,8 +8,10 @@
 import itertools
 import pickle
 from string.templatelib import Template
+import types
 import typing
 import unittest
+import unittest.mock
 from annotationlib import (
     Format,
     ForwardRef,
@@ -1206,6 +1208,84 @@ def evaluate(format, exc=NotImplementedError):
         )
 
 
+class TestCallAnnotateFunction(unittest.TestCase):
+    def _annotate_mock(self):
+        def annotate(format, /):
+            if format == Format.VALUE:
+                return {"x": str}
+            else:
+                raise NotImplementedError(format)
+
+        annotate_mock = unittest.mock.MagicMock(
+            wraps=annotate
+        )
+
+        # Add missing magic attributes needed
+        required_magic = [
+            "__builtins__",
+            "__closure__",
+            "__code__",
+            "__defaults__",
+            "__globals__",
+            "__kwdefaults__",
+        ]
+
+        for attrib in required_magic:
+            setattr(annotate_mock, attrib, getattr(annotate, attrib))
+
+        return annotate_mock
+
+    def test_user_annotate_value(self):
+        annotate = self._annotate_mock()
+
+        annotations = annotationlib.call_annotate_function(
+            annotate,
+            Format.VALUE,
+        )
+
+        self.assertEqual(annotations, {"x": str})
+        annotate.assert_called_once_with(Format.VALUE)
+
+    def test_user_annotate_forwardref(self):
+        annotate = self._annotate_mock()
+
+        new_annotate = None
+        functype = types.FunctionType
+
+        def functiontype_mock(*args, **kwargs):
+            nonlocal new_annotate
+            new_func = unittest.mock.MagicMock(wraps=functype(*args, **kwargs))
+            new_annotate = new_func
+            return new_func
+
+        with unittest.mock.patch("types.FunctionType", new=functiontype_mock):
+            with self.assertRaises(NotImplementedError):
+                annotations = annotationlib.call_annotate_function(
+                    annotate,
+                    Format.FORWARDREF,
+                )
+
+        # Test the direct call
+        annotate.assert_called_once_with(Format.FORWARDREF)
+
+        # Test the call on the function with fake globals
+        new_annotate.assert_called_once_with(Format.VALUE_WITH_FAKE_GLOBALS)
+
+    def test_user_annotate_string(self):
+        annotate = self._annotate_mock()
+
+        with self.assertRaises(NotImplementedError):
+            annotations = annotationlib.call_annotate_function(
+                annotate,
+                Format.STRING,
+            )
+
+        annotate.assert_has_calls([
+            unittest.mock.call(Format.STRING),
+            unittest.mock.call(Format.VALUE_WITH_FAKE_GLOBALS),
+        ])
+
+
 class MetaclassTests(unittest.TestCase):
     def test_annotated_meta(self):
         class Meta(type):