Tevez returned to training on Tuesday after handing in a transfer request that was promptly rejected at the weekend. 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: "I like players who want to play for the manager. I would let him go as long 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 the 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."
According to Rosler, Tevez does not deserve to wear the captain's armband. He said: "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. He has been making strange comments about his future, about his ambitions in football and lately handing in a transfer request. That is disappointing and difficult to understand. I would take the captaincy away from him, 100%."