Tevez was offered another lucrative new deal last month after City's FA Cup final success.
He 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.
"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."