The Argentine returned to Manchester City on Wednesday having served his two-week suspension for allegedly refusing to come on as a substitute during the Champions League defeat to Bayern Munich.
In the aftermath of the match, which City lost 2-0, Mancini hit out at the striker and claimed he would 'never' play for the club under his management ever again.
Lonely place: Carlos Tevez has been training on his own at Manchester City
Journalists attending the pre-planned briefing ahead of the Premier League encounter with Aston Villa at the Etihad Stadium were informed the subject of Tevez's present disciplinary case was off limits.
However when asked today if Tevez had a future at the club following his return, Mancini said: 'I don't know.'
Earlier, a City official had outlined the club's position and warned the press conference would be terminated if questions about Tevez were asked.
'We have been unable to allow questions about Carlos Tevez today, either to Carlos in general, his alleged conduct on the night in question, or the ramifications of that conduct,' said the statement.
'Questions also in relation to his future at the club are strictly off limits today and won't be answered. Breaches of this will result in the press conference being cancelled.'
You wanna be in my gang? Mancini appears to have softened his stance on Tevez
It comes after Sportsmail reported Mancini had persuaded Tevez to meet him in the early hours of Thursday morning in an extraordinary attempt to end their bitter dispute.
Within hours of City announcing their intention on Wednesday to take disciplinary action against the player, Mancini phoned him.
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Tevez was in London on Wednesday, intending to catch the 9pm train to Manchester. Shortly before boarding he received the call from Mancini asking him to go to his house. Tevez's train arrived at around 11pm and he was driven to his manager's home in Alderley Edge.
During the meeting, Mancini told Tevez he would reintegrate him into his first-team squad but only on his own terms. The City boss told Tevez he must apologise privately and publicly to him as well as club chairman Khaldoon Al Mubarak.
Tevez refused because Mancini would not concede any ground despite the player's insistence that, while he did refuse to move from the bench when Mancini ordered him to warm up, he never refused to play. The meeting ended soon after 1am.
Tevez is expected to be fined between four and six weeks' wages and possibly suspended.
Today, the City chief did give an indication Tevez was not in his plans when he addressed how many strikers he had available for the Villa game.
'We have three strikers at this moment,' said Mancini, who has vowed not to take any risks with Sergio Aguero, who has been suffering from an adductor muscle injury.
Mancini assured City supporters not to be worried about their club, and insisted he is feeling no pressure, having been made immune to such issues during his four years at Inter Milan.
Loud and clear: City fans turned on Tevez after the Munich debacle
'If you speak with Rafael Benitez, with Marcello Lippi, with Leonardo, Inter Milan is a strong team for any manager,' he said. 'If you stay there for four years, you are strong enough to be at every club.
'I don't have any problems. I have had experiences in my life. Why should I have any pressure?'
Indeed, Mancini rates himself as an improved operator now to what he was when he first arrived at City almost two years ago.
'I am a better manager now,' he said. 'When you go to another country, you can work with different players in different situations, in a different culture. Every manager can improve. I am sure that I have improved in England.'
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