Tevez is to return to the Etihad Stadium on Tuesday and resume his career with City that has been placed on hold for the last three and a half months following a bust-up with Mancini.
The Argentina striker's refusal to warm up during a Champions League defeat to Bayern Munich at the end of September sparked a cold war between the club and the player.
It appeared at one stage last month Tevez would be shipped out as Inter Milan, AC Milan and Paris St Germain all showed an interest but no move was forthcoming.
With the realisation he needs to be playing football to get his life and future back on track, moves are now being made for the 28-year-old to find a way forward with Mancini.
However, the Italian made it clear following a 1-0 win at Aston Villa that enabled his side to return to the top of the Barclays Premier League, he was still seeking an apology.
If that is forthcoming and the air is cleared, as far as Tevez's team-mates are concerned, they will be glad to see him again in their push for the title over the final 13 matches.
"He is a good player and we'd welcome him back," said winger James Milner when asked by Press Association Sport as to his thoughts on the prospect of Tevez's return.
"He showed how good he was last year (scoring 24 goals). He was fantastic for us.
"What's gone on or what's happening is nothing really to do with the players, but if it gets sorted out, then great.
"It means it's another top player for us to add to the ranks."
Defender Pablo Zabaleta, who concedes to having missed compatriot Tevez, echoed Milner's comments.
"This situation has been crazy for everybody, for the players, the club and especially for Carlos," said Zabaleta.
"If we see him coming back this week, it depends on the manager's decision whether he is given another chance or not.
"As a player, if he comes back he will be another player in the squad.
"We know him, but we have to be very strong in this moment, to be focused on what we are doing."
Speaking to the Manchester Evening News, Zabaleta added: "He would be welcomed by the players, because it was a difficult situation for everybody.
"But most important is that we are doing well as a team."
Tevez's advisor Paul McCarthy has confirmed the player will be back at City on Tuesday, eager to put the past behind him and to play his part in the club clinching the league title.
"He wants to be back playing football, and that's what he's best at doing," said McCarthy.
"He needs to be back, to be pulling on a Manchester City shirt again, to be doing what he does, and that's score goals and help his team.
"He wants to help Manchester City to win the title, and I think Roberto Mancini has opened the door now.
"Once Carlos is back in the country, once Carlos gets his fitness back, I think he will be an asset for City."
The latest development comes following negotiations between City's acting chief executive John MacBeath and Tevez's representative Kia Joorabchian.
Speaking on Sky Sports News, McCarthy added: "There have been some very sensible discussions which have taken place in, probably, the last 10 days and I have to say there has been a thawing on both sides.
"It's been an incredibly difficult time, certainly from Manchester City's side of things.
"But I think now there is an understanding that by far and away the best thing is for Tevez to be back and playing football for Manchester City again."
To aid the situation, it is believed Tevez will drop his appeal to the Premier League against a six-week club fine, totalling around £1.2million.