The 28-year-old is heading back to the Premier League club that he has not played for since September after defying Italian Mancini's instruction to warm up during the Champions League defeat at Bayern Munich.
Speaking for the first time since returning to his homeland without City's permission in November, Tevez gave his version of what happened in Germany.
He said Mancini had been arguing with striker Edin Dzeko who had just been substituted when the manager approached Tevez.
"He saw me on the bench and as he was angry, he sent me again like a dog to warm up. Because he said it to me in a bad tone I refused," Tevez said in an interview with Fox Sports broadcast on Monday.
Mancini said at the time Tevez was "finished" at the league leaders but has since hinted the striker could still play a part in their pursuit of a first league title since 1968.
Tevez said on Monday he would gladly play for the club again if Mancini was serious about having him back, and was aware he would have to pull out all the stops to win over fans who have burned shirts with his name on in anger at his behaviour.
"If I was wrong, I say sorry. I sincerely believe I did not make a mistake," the former City captain added.
"If it's true [Mancini would welcome me back], of course I like that, if it's [meant] for the media, no."
He has pledged to give his all to the club he won the FA Cup with last term but will have raised some eyebrows with criticism of his manager's decision to go public with the saga.
"There the coach made a mistake," Tevez said. "The situation in Bayern could have been kept hidden, managed differently. [Mancini] could have left me out and later said 'Carlos is not well'.
"There are fights but you don't have to air them. We argued many times in the dressing room and on those occasions he didn't say he didn't want me [to play again].
"I had a good relationship with him and I believe he's a winner, he doesn't like to lose, and I'm also like that."
TOP PLAYER
Tevez has been the subject of disciplinary action by the club, over both his refusal to warm up and his subsequent unauthorised departure to his homeland, but relations have thawed and Mancini has suggested he could play again.
"Everyone knows Carlos is a top player," the manager said on Sunday. "If he was here and playing it would be better because Carlos can change games."
With City's early season free-scoring ways slowing down of late, the return of a fit and hungry Tevez - whose talent, goals and work rate once made him a fan favourite - could come at just the right time.
An adviser to Tevez's representative Kia Joorabchian, Paul McCarthy, told Reuters the striker was returning to England and could be playing for City in the next two to three weeks.
"He is due back in England on Tuesday and hopefully will start training this week," McCarthy said.
"He has not just been playing golf in Argentina, he has done a lot of fitness work too but is probably still two or three weeks away from being match-fit.
"He needs to be back and he needs to be pulling on the Manchester City shirt again and doing what he does best, which is scoring goals and helping the team. He could be vital for City over the last nine or 10 games of the season."
If he were to pull on a sky blue shirt once again, Tevez said he would have to be "brilliant" to get fans back on side.
"It's my decision to go back and set myself this challenge: I want to win over the fans again," he said.
"They turned against me after what happened and, for me, they were badly informed. They were told I
