diff --git a/tornado/websocket.py b/tornado/websocket.py
index 2e1eed4728..434626f6f2 100644
--- a/tornado/websocket.py
+++ b/tornado/websocket.py
@@ -1360,7 +1360,7 @@ def __init__(
         subprotocols: Optional[List[str]] = None,
         resolver: Optional[Resolver] = None,
     ) -> None:
-        self.connect_future = Future()  # type: Future[WebSocketClientConnection]
+        self.connect_future = Future()  # type: Union[Future[WebSocketClientConnection], None]
         self.read_queue = Queue(1)  # type: Queue[Union[None, str, bytes]]
         self.key = base64.b64encode(os.urandom(16))
         self._on_message_callback = on_message_callback