Tevez's advisor Kia Joorabchian has now opened preliminary discussions with Paris St Germain over a potential move for the former City captain.
City have also been involved in recent dialogue with Inter Milan over the 27-year-old striker while AC Milan withdrew from talks with the club.
Tevez has not played for City since September and is currently in his native Argentina awaiting a possible transfer.
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."
Mancini was on Friday asked 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 [Thursday]. Maybe today [Friday] or tomorrow [Saturday], 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."
Mancini has created headlines himself in recent weeks by waving imaginary cards at officials during matches.
The most recent incidence occurred at Wigan when Mancini wanted Maynor Figueroa sent off for denying a goalscoring opportunity with a handball.
Earlier this month he called for Liverpool's Martin Skrtel to be dismissed by making a similar gesture and then accused Manchester United's Wayne Rooney of doing the same against City.
Mancini has been criticised for his actions but he has blamed cultural differences and does not think the matter is a big deal.
He said: "I am happy that it is something for people to talk about. I did nothing."