Argentina international Tevez was given compassionate leave and allowed to return to his homeland earlier this month due to complications with his wife Vanesa's pregnancy.
The couple's baby daughter has been in intensive care after being born prematurely and until this week it had been unclear when Tevez was likely to come back.
Return to action: Manchester City's Argentinian striker Carlos Tevez
Mancini appeared to be at a loss on the matter following Sunday's 0-0 draw with Liverpool, but yesterday Tevez's adviser Kia Joorabchian insisted the player had kept City informed of developments and was hopeful of returning for Saturday's trip to Chelsea in the Barclays Premier League.
Today Mancini indicated that, having spoken to Tevez, he was convinced he would be available for the match at Stamford Bridge.
'I spoke with him yesterday and I think that he will come back on Thursday or Friday morning,' Mancini said, before adding: 'I am sure.'
He continued: 'It is important Carlos comes back Thursday or Friday so he can play against Chelsea. He said to me that every day he has been training in Argentina, every morning.
'He had a serious problem but now I think he resolved his problem.'
While Manchester City are optimistic of Tevez's return, no flight to England has been booked.
City travel to Stoke tomorrow for an FA Cup fifth-round replay which will be the fourth game Tevez - their 19-goal top-scorer - will have missed, a sequence in which the team has struggled for form and so far failed to pick up a win.
Sharpshooter: Tevez has 19 goals this season
Reports had suggested that the situation may have soured relations between Tevez and Mancini, who admitted last week to having a disagreement with Craig Bellamy over the management of the Welsh forward's long-standing knee injury.
But the Italian manager was adamant he retains the backing of his squad and claimed that any disputes that had gone on were nothing out of the ordinary.
He said: 'For me it is not a problem. Usually I do not read the newspapers, but I have read (them) and for me everything is normal.
'I can speak with my players because we don't have the same things, but this is normal. It is not a problem, not a serious problem for me.'
Asked if he felt he has the full respect and confidence of the players, Mancini said: 'Yes, absolutely. I have respect for the players always, but when I work I want to work very well and I want to work because I want to win. I do not work only to enjoy football.
'This is different. If we are going to win, we must change our mentality, we must work very well, we must think when we work and this is most important.
'But I haven't got any problem with the players - or (they are) normal problems that a manager has with his team.'
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