diff --git a/pandas-stubs/core/frame.pyi b/pandas-stubs/core/frame.pyi
index 3c5b2010b..1a91f717c 100644
--- a/pandas-stubs/core/frame.pyi
+++ b/pandas-stubs/core/frame.pyi
@@ -2344,9 +2344,18 @@ class DataFrame(NDFrame, OpsMixin, _GetItemHack):
         axis: Axis | None = ...,
         level: Level | None = None,
     ) -> Self: ...
+    @overload
     def max(
         self,
-        axis: Axis | None = 0,
+        axis: None,
+        skipna: _bool | None = True,
+        numeric_only: _bool = False,
+        **kwargs: Any,
+    ) -> Scalar: ...
+    @overload
+    def max(
+        self,
+        axis: Axis = 0,
         skipna: _bool | None = True,
         numeric_only: _bool = False,
         **kwargs: Any,
diff --git a/tests/test_frame.py b/tests/test_frame.py
index 521d4b896..e52d53c58 100644
--- a/tests/test_frame.py
+++ b/tests/test_frame.py
@@ -826,6 +826,7 @@ def test_types_max() -> None:
     df = pd.DataFrame(data={"col1": [2, 1], "col2": [3, 4]})
     check(assert_type(df.max(), pd.Series), pd.Series)
     check(assert_type(df.max(axis=0), pd.Series), pd.Series)
+    check(assert_type(df.max(axis=None), Scalar), np.int64)
 
 
 def test_types_quantile() -> None: