diff --git a/grpclib/protocol.py b/grpclib/protocol.py
index 314449c..66f66c1 100644
--- a/grpclib/protocol.py
+++ b/grpclib/protocol.py
@@ -476,6 +476,8 @@ def __terminated__(self, reason: str) -> None:
 
     @property
     def closable(self) -> bool:
+        if self._transport.is_closing():
+            return False
         if self._h2_connection.state_machine.state is ConnectionState.CLOSED:
             return False
         stream = self._h2_connection.streams.get(self.id)