diff --git a/sanic/server/protocols/base_protocol.py b/sanic/server/protocols/base_protocol.py
index bf1b3c15..2e8a115e 100644
--- a/sanic/server/protocols/base_protocol.py
+++ b/sanic/server/protocols/base_protocol.py
@@ -90,8 +90,9 @@ class SanicProtocol(asyncio.Protocol):
         if self.transport:
             self.transport.close()
             if timeout is None:
-                timeout = self.app.config.GRACEFUL_SHUTDOWN_TIMEOUT
-            self.loop.call_later(timeout, self.abort)
+                self.abort()
+            else:
+                self.loop.call_later(timeout, self.abort)
 
     def abort(self):
         """
diff --git a/sanic/server/protocols/http_protocol.py b/sanic/server/protocols/http_protocol.py
index 6e30fc0f..689db2ac 100644
--- a/sanic/server/protocols/http_protocol.py
+++ b/sanic/server/protocols/http_protocol.py
@@ -109,6 +109,7 @@ class HttpProtocol(HttpProtocolMixin, SanicProtocol, metaclass=TouchUpMeta):
         "_http",
         "_exception",
         "recv_buffer",
+        "_callback_check_timeouts",
     )
 
     def __init__(
@@ -135,6 +136,7 @@ class HttpProtocol(HttpProtocolMixin, SanicProtocol, metaclass=TouchUpMeta):
         if "requests_count" not in self.state:
             self.state["requests_count"] = 0
         self._exception = None
+        self._callback_check_timeouts = None
 
     async def connection_task(self):  # no cov
         """
@@ -214,7 +216,7 @@ class HttpProtocol(HttpProtocolMixin, SanicProtocol, metaclass=TouchUpMeta):
                     )
                     / 2
                 )
-                self.loop.call_later(max(0.1, interval), self.check_timeouts)
+                self._callback_check_timeouts = self.loop.call_later(max(0.1, interval), self.check_timeouts)
                 return
             cancel_msg_args = ()
             if sys.version_info >= (3, 9):
@@ -223,6 +225,19 @@ class HttpProtocol(HttpProtocolMixin, SanicProtocol, metaclass=TouchUpMeta):
         except Exception:
             error_logger.exception("protocol.check_timeouts")
 
+    def close(self, timeout: Optional[float] = None):
+        """
+        Requires to prevent checking timeouts for closed connections
+        """
+        if timeout is not None:
+            super().close(timeout=timeout)
+            return
+        if self._callback_check_timeouts:
+            self._callback_check_timeouts.cancel()
+            if self.transport:
+                self.transport.close()
+                self.abort()
+
     async def send(self, data):  # no cov
         """
         Writes HTTP data with backpressure control.