Bellamy has been sidelined with a knee injury since the beginning of the month and although there was a suggestion that he could return for the match on Thursday night he has not travelled to Denmark with the rest of the City squad.
"We took the decision on Tuesday night that he wouldn't travel," City manager Mark Hughes told the club's official website.
"We thought it would be better for him to stay at home and try to get himself fit for Sunderland on Sunday.
"He's been doing work with the physios, and hopefully if he doesn't have a reaction he may well be an option against Sunderland.
"He felt a bit of discomfort yesterday but we are told it's settled down now."