Tevez, who has not played for City since last September due to his infamous dispute with the club, has been training for the past month with a view to a first-team comeback.
The Argentinian has made two appearances for the reserves since returning from his unauthorised leave and Mancini believes he could now be close to match fitness.
The 28-year-old's return could give the team a timely lift after defeat at Swansea on Sunday saw them surrender top spot in the Barclays Premier League to arch-rivals Manchester United.
City are not in league action again until Chelsea visit the Etihad Stadium next Wednesday, by which time United could be four points ahead.
Asked if Tevez could be available for that game, Mancini said: "We will see in the next week. It depends on Carlo.
"If Carlo is okay then probably, but it depends on a lot of things."
Mancini was speaking at a press conference to preview the second leg of his side's Europa League last-16 tie against Sporting Lisbon on Thursday.
Tevez, wearing a blue and white hat, trained with the squad on Wednesday morning but is not eligible to play in Europe having not been registered.
Another player set to miss out as City seek to overturn a 1-0 first-leg deficit on Thursday is Gareth Barry.
The England midfielder, who appeared to show dissent when surprisingly substituted in the first half at Swansea, has been troubled by a back injury in the past month and is likely to be rested.
He missed the game against Blackburn on February 25 with the problem but did recover sufficiently to play for England four days later.
Mancini said: "Gareth has had a problem with his back for 20 days. He can't run well.
"When he went to the national team he had a problem.
"On Sunday he didn't play well but I think that is because he had a problem.
"We will see for him in the next days but probably he needs another two or three days' rest.
"These players are not like robots, they need to rest.
"Instead they go to the national team instead of resting for two or three days.
"It is impossible for these players to play for 10 months every three days."
Captain Vincent Kompany is unlikely to return before the trip to Stoke on March 24 due to a calf injury but fellow defender Joleon Lescott could be on the bench on Thursday after a calf problem.
Right-back Pablo Zabaleta, also out with a hamstring injury, could be back in contention to face Chelsea.