diff --git a/yt_dlp/networking/_websockets.py b/yt_dlp/networking/_websockets.py
index 46d5f88afe..46b6c7ccd3 100644
--- a/yt_dlp/networking/_websockets.py
+++ b/yt_dlp/networking/_websockets.py
@@ -265,6 +265,6 @@ def __init__(self, ssl_context: ssl.SSLContext):
         self.ssl_context = ssl_context
 
     def wrap_socket(self, sock, server_hostname=None):
-        if isinstance(sock, ssl.SSLSocket):
+        if isinstance(sock, ssl.SSLSocket) or WebsocketsSSLTransport:
             return WebsocketsSSLTransport(sock, self.ssl_context, server_hostname=server_hostname)
         return self.ssl_context.wrap_socket(sock, server_hostname=server_hostname)