Tevez, who is currently AWOL in Argentina, has been linked with a move to AC Milan, Inter Milan and PSG during the January transfer window but despite ongoing negotiations with his agent Kia Joorabchian, no deal has yet been struck.
Serie A leaders Milan recently withdrew from transfer talks with City as the Premier League club are demanding a sizeable transfer fee and with the options dwindling, Mancini is desperate for a deal to be done.
Mancini said: "I hope this will finish very quickly. I don't know [the latest]. I think he has talked with PSG and Inter, but not Milan. I hope for him everything can finish very quickly.''
The Italian, speaking at a press conference to preview Sunday's Premier League clash with Tottenham, said there was no way Tevez could return to City.
"This is impossible. Carlos doesn't want to stay," he said. "It is important for him to start to play because he is a football player. It is now three months that he hasn't played and this is not good for him.''
Meanwhile, City defender Nedum Onuoha is edging closer to a possible move to QPR.
The 25-year-old academy graduate appeared as a substitute in the Premier League leaders' win at Wigan on Monday but has otherwise struggled for opportunities since returning from a loan at Sunderland.
Mancini said: "I don't know [the latest]. They were talking yesterday. Maybe today or tomorrow, it is possible.
"Nedum deserves to play. He is a good guy and if he stays here he will maybe play one or two games. That is not enough for a young player.''