The Bluebirds had made a “tentative verbal request” to Chelsea, hoping to include the influential forward, but the Premier League side refused to provide the required written consent.
Kellyman joined Cardiff on a season-long loan in September to gain first-team experience after recovering from a serious hamstring injury, and will now watch the match from the stands.
While FA and Premier League rules prevent loanees from facing their parent clubs, EFL Cup regulations allow it if special permission is granted.
The 20-year-old has been pivotal for League One leaders this season, featuring 17 times and scoring twice. He called playing against Chelsea a “great opportunity” but must accept the decision.
