Tevez, 28, has not played for City since his refusal to follow the instructions of coach Roberto Mancini and warm up during the Champions League defeat by Bayern Munich in September.
His last appearance was in a League Cup win over Birmingham City on September 21 and that looked like being the last time he ever played for City after Mancini said he was "finished" at the club.
Tevez has been back in Argentina on unauthorised leave since November, but Paul McCarthy, an advisor to Tevez's representative Kia Joorabchian, told Reuters the player was returning to England.
"He is due back in England on Tuesday and hopefully will start training this week. 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," McCarthy said.
"Roberto Mancini has more than opened the door for him and now it's a case of getting his fitness back.
"There have been a lot of very productive, sensible discussions over the last 10 days or so and a thawing in relations on both sides.
"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."
Apart from a couple of occasions when United have topped the table because they have played before City during the weekend, Mancini's men have led the standings since mid-October.
Although they have stuttered slightly in recent weeks, losing three of their last 11 league matches, the 1-0 win at Aston Villa on Sunday kept City two points clear of United with 13 matches to play.
Tevez was City's top league scorer in the 2009/10 season with 23 goals and again last season with 20 goals, but failed to score in the five appearances he made in all competitions before the Munich fallout.
His unauthorised absence in Argentina has cost him millions in lost wages and he has been fined six weeks' wages for gross misconduct over his disappearance home without permission.
He was also eager for a move away from City in the January transfer window but possible moves to AC Milan, Inter Milan and Paris Saint-Germain all failed to materialise.
Mancini strongly hinted on Sunday that Tevez could still play a role for City.
"Everyone knows Carlos is a top player. If he was here and playing it would be better, because Carlos can change games," Mancini said.
