But Rosler, who played 177 games for the club, told BBC Radio Manchester: "I'd take the captaincy away, 100%.
"In the long term it is important that every player is totally committed to City. I would let him go as long as the price is right."
City are believed to have paid Tevez's advisors, who owned his economic rights, £25.5m to sign him in 2009 following a two-year spell with rivals Manchester United.
But less than 17 months into a five-year contract, the 26-year-old claimed his relations with "certain executives" at City had "broken down beyond repair".
Tevez reportedly said that family reasons were behind his decision to look for a move and stressed that he had "no personal issue" with manager Roberto Mancini, despite their
touchline altercation
during a 1-0 victory over Bolton on 4 December.
BBC Sport understands the former Boca Juniors, Corinthians and West Ham player will not be sold in January, although Rosler feels City's wealth would ensure an adequate replacement could be found if he were to depart.
The Eastlands outfit was taken over by the Abu Dhabi United Group in September 2008 and owner Sheikh Mansour has spent heavily on transfers and wages in his first two years at helm.
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Some may understandably ask precisely what City expected when they signed the Argentine given Joorabchian and Tevez are no strangers to controversy
"City have to get the money back for him," insisted Rosler, who recently suggested losing Tevez
could have a "disastrous affect" on City's bid to become a major force in European football.
"They are fortunately in a very good position regarding the owners and replacing Tevez. You should have a dressing room with more harmony and spirit with everyone driving in the same direction," he added.
"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 was handed the captain's armband by Mancini last summer but has previously criticised the Italian's training methods and the pair
clashed in the dressing room
at half-time during October's victory against Newcastle.
And the striker also worried supporters by suggesting he could retire from football completely to enable him to spend more time with his wife and children in Argentina.
"City supporters idolise Tevez because of the way he is playing and the way he is leading by example on the field," stated Rosler.
"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."
Tevez is expected to miss City's Europa League match against Juventus on Thursday, and Mancini might also be without fellow striker Mario Balotelli.
The former Inter Milan forward
suffered racial abuse
at the hands of some Juve supporters during Inter's trip to the Olympic Stadium last season.
He was also targeted by a number of his own fans during
Italy's friendly against Romania
in Austria in November.
If Tevez and Balotelli are missing, Mancini will be short of attacking options as Roque Santa Cruz is not in their squad list, leaving Emmanuel Adebayor and Jo as the only senior strikers.
Mancini apparently made the decision to rest Tevez for the Juve match before last weekend, knowing the game was a dead rubber.
City and Lech Poznan are already through to the next stage of the tournament with Juventus, now second in Serie A, eliminated.
Mancini is already back in Italy for a minor eye operation and will probably not speak to Tevez before Friday, although his first thoughts on the situation should come at a press conference in Turin on Wednesday.
Source: BBC Sport
Source: BBC Sport