City play Everton on Monday with Mancini considering handing the armband to Kolo Toure or Vincent Kompany.
The manager is yet to inform the club of his decision, but senior officials believe he is most likely to reinstate Toure as skipper.
The defender was made captain under Mark Hughes but replaced by Tevez in the summer in a bid to make the Argentine stay at Eastlands.
Despite the outcome of today's meeting between Tevez and Mancini, we need to give Tevez the same cheers when we hear his name as any other week. We need to show Tevez that he is still wanted and very much needed The Return of Mancinis Scarf On Sunday morning, Toure was still unaware of whether he would be captain against Everton, but Mancini is believed to regard him as the best option until Tevez's future is resolved.
City rejected a written transfer request from Tevez last week and have made it clear they will not sell him in January, with Eastlands football administrator Brian Marwood declaring on Friday he expects the striker to honour his contract, which runs until July 2014.
Manager Mancini has also spoken publicly of his hopes of convincing Tevez his future lies with City, who are third in the Premier League table on 32 points - two points behind leaders Manchester United but having played a game more.
I want to talk to Tevez - Mancini
"He is our player and I hope he continues to play and score for us," said Mancini.
Tevez, 26, claimed an irreparable breakdown in his relationship with "certain executives" was the basis for his desire to leave City.
He was not in the party that travelled to Italy for Thursday's 1-1 Europa League draw with Juventus, with Mancini instead giving a number of fringe players a run-out with qualification to the last 32 already assured.
Marwood has suggested that some of the figures surrounding Tevez, who is advised by Iranian Kia Joorabchian, may be agitating for a move.
Tevez situation will not affect team - Platt
However, Joorabchian, who claims to have tried to talk Tevez into staying, has said that the striker's desire to leave stems in part from City's failure to qualify for this season's Champions League.
Tevez joined City in 2009 following a two-year spell with rivals Manchester United.
He scored 29 goals in his debut season and has managed 10 in 18 appearances since Mancini handed him the captaincy prior to the start of the current campaign.
But less than 17 months into a five-year contract, the former Boca Juniors, Corinthians and West Ham forward asked to leave.