Tevez hasn't played for City since he refused to warm up during the Champions League defeat to Bayern Munich in September but the Argentine forward is expected back in England on Tuesday after seeing a move away from Eastlands fail to materialise last month.
Mancini had initially vowed Tevez would never play for the club again.
However, speaking after Sunday's 1-0 victory at Aston Villa, which moved City back to the top of the Premier League, the Italian indicated he is prepared to forgive and forget and pick the player again.
On the weekend the Luis Suarez and Patrice Evra saga took a fresh twist over the Liverpool forward's failure to shake hands with the Manchester United defender, Mancini said: "I think it is a bad moment to talk about shaking hands, but yes. I always forgive people, every time.
"It's up to him. Carlos knows everything. We are here, we didn't change city in these three months, so we are here and Carlos knows this.
"Carlos is a City player. For three months we have been expecting him back.
"I am there, Carlos knows. I spoke to him one week after Munich, Carlos knows everything. I can't say any more.
"Would I like him to apologise? This is normal I think. And after, Carlos can train and Carlos can play if his condition is good."
Meanwhile, Mancini hailed his players after Joleon Lescott's second-half strike ended Villa's stubborn resistance in a game City completely dominated.
"I'm very pleased with all the players because I think they did a very good performance," he said.
"They played very well. We conceded only one chance. We would have been really unlucky if they had scored with the last chance. We played very well and we had a lot more possession.
"It is not easy to play away against Aston Villa they are a good team. But if you don't score two goals then maybe in the end you can be at some risk."
The win enabled City to restore their two-point lead at the top of the Premier League after Manchester United had climbed above them for 24 hours with a victory over Liverpool on Saturday.
Mancini was delighted with the character shown by his squad in grinding out the victory, however he insisted their neighbours remain the side to beat.
"For us December and January were difficult months because we had players injured, players banned and players away," Mancini said.
"Now we are in February and we are still on the top. I think next week we will have all the players and this is very important for us.
"But to stay on the top with Manchester United and Tottenham, I think that we have to be very strong because United are still better than us.
"United have won everything in the last 10 years. Until we win the title United are better."
Meanwhile, Villa manager Alex McLeish revealed he expects centre-back Richard Dunne to be out for a prolonged spell with a shoulder injury.
"I believe he will be out for at least a month, that's serious enough," McLeish said.
"He's definitely damaged his shoulder which is part of the bad luck we've been having recently."
McLeish had no complaints with the display from his players and felt they were unfortunate to depart with nothing to show for their efforts.
"We had a game plan and I thought the players did really well in executing it," he said.
"If you open up early and leave yourself wide open against City they will destroy you. I thought the players executed the plan really well and the discipline was fantastic.
"We were never going to go gung-ho against City because we just don't have the players to do that."