The 27-year-old handed in a transfer request midway through last season amid reports that he was eager to leave England and be closer to his family who do not live with him, but later reversed that decision.
Tevez, who was offered another lucrative new deal last month after City's FA Cup final success, said in the News of the World: 'Sheikh Mansour has made a lot of sacrifices to keep me and if I stay at City, it will be for him.
Goodbye for good? Tevez's future at City remains undecided
'He signed me, he wants to keep me but, at the same time, he has told me to do whatever I need to do to be happy.
'He has told me, "If you want to leave, then you can go". There is no deadline - it's down to me. They offered me a new contract in December but I didn't want to extend it.
'At the end of the season they offered me another new deal but at the moment I don't know whether I will accept it.'
Tevez has no great affinity with Manchester despite having spent nearly four years in the city, first with a two-year spell at United from 2007.
Hero worship: Tevez has helped City to silverware following his much hyped switch across Manchester
He reportedly told Argentinian television channel Telefe: There is nothing to do in Manchester. The problem is I'm still speaking very poor English.
'When I finish my contract I will not return to Manchester ever - not even on holiday.'
The Argentinian has no remorse about having asked to leave the club six months ago, blaming members of the City board for his actions.
'I have no regrets whatsoever about my transfer request,' he continued. 'It was a situation that some people on the board created. They promised something for six months and didn't deliver.
'So, after six months of promises, they don't do something - why should I believe them now? I don't.I will never speak to these people again. I still feel the same way.
Family ties: Tevez has made no secret he dislikes life in Manchester despite the good relationship he has with his team-mates
'I deal direct with Sheikh Mansour - no-one else. It makes no difference to my future, as they don't mean anything to me.'
Despite being team captain and a key man in City's surge towards Champions League football and the FA Cup, the player continued to be linked with a move abroad.
Tevez's two daughters live with their mother in Argentina during the football season.
He added: 'No amount of money, no cars and the lifestyle can make up for the moment when I leave my two daughters at the airport.
'Do you think money solves everything? It solves nothing. People think I should be happy because I have everything but I can't buy time with my daughters and my family.'
Fond farewell: City owner Sheikh Mansour has told Tevez he can leave if he wants to
Asked whether Tevez would remain with City, his agent Kia Joorabchian told BBC Radio 5 Live's Sportsweek programme: 'His family come first. He will be in Argentina. He will sit down and talk to his family.
'Until he resolves that issue he's not making a final determination on his future. What I can tell you is he is very happy at Manchester City. He has been happy at Manchester City.
'He's resolved his problems he had earlier in the year with certain members of the board. If he can resolve his family issues then why not?'
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