diff --git a/fastapi/dependencies/utils.py b/fastapi/dependencies/utils.py
index 2abae433b..262dba6fd 100644
--- a/fastapi/dependencies/utils.py
+++ b/fastapi/dependencies/utils.py
@@ -209,7 +209,7 @@ def get_flat_params(dependant: Dependant) -> List[ModelField]:
     return path_params + query_params + header_params + cookie_params
 
 
-def get_typed_signature(call: Callable[..., Any]) -> inspect.Signature:
+def _get_signature(call: Callable[..., Any]) -> inspect.Signature:
     if sys.version_info >= (3, 10):
         try:
             signature = inspect.signature(call, eval_str=True)
@@ -219,6 +219,11 @@ def get_typed_signature(call: Callable[..., Any]) -> inspect.Signature:
             signature = inspect.signature(call)
     else:
         signature = inspect.signature(call)
+    return signature
+
+
+def get_typed_signature(call: Callable[..., Any]) -> inspect.Signature:
+    signature = _get_signature(call)
     unwrapped = inspect.unwrap(call)
     globalns = getattr(unwrapped, "__globals__", {})
     typed_params = [
@@ -244,15 +249,7 @@ def get_typed_annotation(annotation: Any, globalns: Dict[str, Any]) -> Any:
 
 
 def get_typed_return_annotation(call: Callable[..., Any]) -> Any:
-    if sys.version_info >= (3, 10):
-        try:
-            signature = inspect.signature(call, eval_str=True)
-        except NameError:
-            # Handle type annotations with if TYPE_CHECKING, not used by FastAPI
-            # e.g. dependency return types
-            signature = inspect.signature(call)
-    else:
-        signature = inspect.signature(call)
+    signature = _get_signature(call)
     unwrapped = inspect.unwrap(call)
     annotation = signature.return_annotation