Tevez returned to training on Tuesday after handing in a transfer request that was promptly rejected at the weekend and Rosler, who remains a popular figure among the fans after scoring 64 goals in 177 appearances for the club, is baffled by the Argentina international's behaviour.
He told BBC Radio Manchester: "City supporters idolise Tevez because of the way he is playing and the way he is leading by example on the field. But we have seen the other side when he is not living up to his responsibility as club captain off the field. That is disappointing and difficult to understand. I would take the captaincy away from him, 100%."
He added: "I like players who want to play for the manager. I would let him go as long as the price is right. City have to get the money back for him.
"They are fortunately in a very good position regarding the owners and replacing Tevez. In the long term it is important that every player is totally committed to City.
"You should have a dressing room with more harmony and spirit with everyone driving in same direction. Look at Chelsea and Manchester United, when they were winning titles there was not so much noise as there is coming out of the City dressing room."
Tevez is expected to skip City's Europa League match against Juventus on Thursday - and so too could Mario Balotelli.
Manager Roberto Mancini has apparently had a change of heart, according to reports in Italy, after initially saying the former Inter Milan striker would travel.
Balotelli, 20, suffered racist abuse at the hands of some Juventus supporters when an Inter player last season. He was also targeted by a number of Italy fans during a recent friendly against Romania in Austria.
With Tevez and Balotelli missing Mancini would be short of attacking options as Roque Santa Cruz is not on their squad list. It would leave Emmanuel Adebayor and Jo as the senior strikers.