diff --git a/jupyter_server/services/kernels/connection/channels.py b/jupyter_server/services/kernels/connection/channels.py
index 13beab3cc3..9bc06236e3 100644
--- a/jupyter_server/services/kernels/connection/channels.py
+++ b/jupyter_server/services/kernels/connection/channels.py
@@ -4,7 +4,7 @@
 import weakref
 from concurrent.futures import Future
 from textwrap import dedent
-from typing import MutableSet
+from typing import Dict as Dict_t, MutableSet
 
 from jupyter_client import protocol_version as client_protocol_version
 from tornado import gen, web
@@ -21,6 +21,7 @@
 
 from jupyter_server.transutils import _i18n
 
+from ..websocket import KernelWebsocketHandler
 from .abc import KernelWebsocketConnectionABC
 from .base import (
     BaseKernelWebsocketConnection,
@@ -103,7 +104,7 @@ def write_message(self):
     # class-level registry of open sessions
     # allows checking for conflict on session-id,
     # which is used as a zmq identity and must be unique.
-    _open_sessions: dict = {}
+    _open_sessions: Dict_t[str, KernelWebsocketHandler] = {}
     _open_sockets: MutableSet["ZMQChannelsWebsocketConnection"] = weakref.WeakSet()
 
     _kernel_info_future: Future
@@ -391,7 +392,7 @@ def close(self):
     def disconnect(self):
         self.log.debug("Websocket closed %s", self.session_key)
         # unregister myself as an open session (only if it's really me)
-        if self._open_sessions.get(self.session_key) is self:
+        if self._open_sessions.get(self.session_key) is self.websocket_handler:
             self._open_sessions.pop(self.session_key)
 
         if self.kernel_id in self.multi_kernel_manager:
@@ -536,16 +537,6 @@ def _reserialize_reply(self, msg_or_list, channel=None):
         else:
             return json.dumps(msg, default=json_default)
 
-    def select_subprotocol(self, subprotocols):
-        preferred_protocol = self.kernel_ws_protocol
-        if preferred_protocol is None:
-            preferred_protocol = "v1.kernel.websocket.jupyter.org"
-        elif preferred_protocol == "":
-            preferred_protocol = None
-        selected_subprotocol = preferred_protocol if preferred_protocol in subprotocols else None
-        # None is the default, "legacy" protocol
-        return selected_subprotocol
-
     def _on_zmq_reply(self, stream, msg_list):
         # Sometimes this gets triggered when the on_close method is scheduled in the
         # eventloop but hasn't been called.
diff --git a/jupyter_server/services/kernels/websocket.py b/jupyter_server/services/kernels/websocket.py
index 2806053a98..be3e021548 100644
--- a/jupyter_server/services/kernels/websocket.py
+++ b/jupyter_server/services/kernels/websocket.py
@@ -14,7 +14,7 @@
 
 
 class KernelWebsocketHandler(WebSocketMixin, WebSocketHandler, JupyterHandler):
-    """The kernels websocket should connecte"""
+    """The kernels websocket should connect"""
 
     auth_resource = AUTH_RESOURCE
 
@@ -75,6 +75,16 @@ def on_close(self):
         self.connection.disconnect()
         self.connection = None
 
+    def select_subprotocol(self, subprotocols):
+        preferred_protocol = self.connection.kernel_ws_protocol
+        if preferred_protocol is None:
+            preferred_protocol = "v1.kernel.websocket.jupyter.org"
+        elif preferred_protocol == "":
+            preferred_protocol = None
+        selected_subprotocol = preferred_protocol if preferred_protocol in subprotocols else None
+        # None is the default, "legacy" protocol
+        return selected_subprotocol
+
 
 default_handlers = [
     (r"/api/kernels/%s/channels" % _kernel_id_regex, KernelWebsocketHandler),