The 28-year-old, who missed much of last season due to a dispute with manager Roberto Mancini, has 18 months remaining on his deal and claims the club want him to stay until 2016.
"I've one year left on my deal and City want me to sign for two more seasons. I'll think about it," said Tevez, quoted in The Sun.
"This year is different from last, when I wanted to end the contract with City. I'm happy here as they're treating me well.
"Sometimes I play, sometimes I don't, but that's OK."
A new deal for the former Manchester United and West Ham forward would complete a remarkable turnaround for the player at the Etihad Stadium after last season's lengthy absence.
But the link up with fellow Argentina international Sergio Aguero looks to have helped Tevez feel at home at City once again.
He added: "We are having a good time with him not only on the pitch but also outside as we play golf together."