diff --git a/sanic/server/protocols/base_protocol.py b/sanic/server/protocols/base_protocol.py
index 4e7540c6..63d4bfb5 100644
--- a/sanic/server/protocols/base_protocol.py
+++ b/sanic/server/protocols/base_protocol.py
@@ -81,13 +81,24 @@ class SanicProtocol(asyncio.Protocol):
         self._data_received.clear()
         await self._data_received.wait()
 
-    def close(self):
+    def close(self, timeout: Optional[float] = None):
+        """
+        Attempt close the connection.
+        """
+        # Cause a call to connection_lost where further cleanup occurs
+        if self.transport:
+            self.transport.close()
+            if timeout is None:
+                timeout = self.app.config.GRACEFUL_SHUTDOWN_TIMEOUT
+            self.loop.call_later(timeout, self.abort)
+
+    def abort(self):
         """
         Force close the connection.
         """
         # Cause a call to connection_lost where further cleanup occurs
         if self.transport:
-            self.transport.close()
+            self.transport.abort()
             self.transport = None
 
     # asyncio.Protocol API Callbacks #
diff --git a/sanic/server/runners.py b/sanic/server/runners.py
index c28c525e..39d8f736 100644
--- a/sanic/server/runners.py
+++ b/sanic/server/runners.py
@@ -180,7 +180,7 @@ def serve(
             if hasattr(conn, "websocket") and conn.websocket:
                 coros.append(conn.websocket.close_connection())
             else:
-                conn.close()
+                conn.abort()
 
         _shutdown = asyncio.gather(*coros)
         loop.run_until_complete(_shutdown)