diff --git a/stdlib/functools.pyi b/stdlib/functools.pyi
index 10c46f42e..0c4d1d2f3 100644
--- a/stdlib/functools.pyi
+++ b/stdlib/functools.pyi
@@ -91,14 +91,14 @@ class _SingleDispatchCallable(Generic[_T]):
     # @fun.register(complex)
     # def _(arg, verbose=False): ...
     @overload
-    def register(self, cls: type, func: None = ...) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+    def register(self, cls: Type[Any], func: None = ...) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
     # @fun.register
     # def _(arg: int, verbose=False):
     @overload
     def register(self, cls: Callable[..., _T], func: None = ...) -> Callable[..., _T]: ...
     # fun.register(int, lambda x: x)
     @overload
-    def register(self, cls: Type, func: Callable[..., _T]) -> Callable[..., _T]: ...
+    def register(self, cls: Type[Any], func: Callable[..., _T]) -> Callable[..., _T]: ...
     def _clear_cache(self) -> None: ...
     def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
 
@@ -110,11 +110,11 @@ if sys.version_info >= (3, 8):
         func: Callable[..., _T]
         def __init__(self, func: Callable[..., _T]) -> None: ...
         @overload
-        def register(self, cls: Type, method: None = ...) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
+        def register(self, cls: Type[Any], method: None = ...) -> Callable[[Callable[..., _T]], Callable[..., _T]]: ...
         @overload
         def register(self, cls: Callable[..., _T], method: None = ...) -> Callable[..., _T]: ...
         @overload
-        def register(self, cls: Type, method: Callable[..., _T]) -> Callable[..., _T]: ...
+        def register(self, cls: Type[Any], method: Callable[..., _T]) -> Callable[..., _T]: ...
         def __call__(self, *args: Any, **kwargs: Any) -> _T: ...
     class cached_property(Generic[_T]):
         func: Callable[[Any], _T]