Bridge went out on loan to West Ham for the second half of last season but returned to City once the Hammers got relegated.
It was expected he would leave the club in the summer with Mancini looking to trim the wage bill, but the Italian stated that the left-back decided to stay despite interest from the Championship and Celtic in the SPL.
"I don't understand why there are some players that have a chance to go and play, maybe not in the Premier League but in the Championship, and don't," he said.
"I don't know why you would want to stay at a club where you can't play.
"When we are young and start to play football we don't play for money, we play because we like football. Every player should have this target in mind - to play football.
"Wayne is a good guy, but he had two or three chances in the summer, including Celtic, who are an important team.
"He trains with us sometimes and sometimes with the young players but I hope, for him, he leaves in January because it's difficult for a player to stay training every day."
A further issue Mancini has is the Africa Cup of Nations next month, which will see him lose Kolo and Yaya Toure of the Ivory Coast.
Although they will still be around for the Manchester derby against United in the FA Cup, the City boss admitted he is unlikely to have them available for the match against Wigan a week later on January 16.
"I think they will leave after United, two weeks before the start of the African Cup," Mancini added.
"If we can find another solution with the Ivory Coast federation, that will be good, but it is difficult."
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