Tevez's advisor Kia Joorabchian has now opened preliminary discussions with Paris St Germain over a potential move for the former City captain and the league leaders have also been involved in recent dialogue with Inter Milan over the 27-year-old striker.
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."
Tevez has not played for City since September and is currently in his native Argentina awaiting a possible transfer.
Mancini was asked on Friday if Tevez could return to the City team if a move fails to materialise before the end of the January transfer window.
The Italian, speaking at a press conference to preview Sunday's Barclays Premier League clash with Tottenham, said: "This is impossible. Carlos doesn't want to stay.
"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."
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."