Tevez has expressed a desire to leave the English Premier League club after two seasons in order to be near his family in South America. He remains with Manchester City after an agreement on a move to Corinthians was unable to be worked out.
"At the moment, Carlos is still a City player," Mancini said. "In the future, we will see what can happen. For us, Carlos is an important player."
Mancini said he has yet to speak with Tevez but respects the captain's wish to play closer to his family. The Manchester City manager said the uncertainty isn't affecting the way he is preparing for the season.
"Carlos wants to leave for his family," Mancini said. "Only because of this the, club accepts it. I think it's because we respect his reason."
Tevez appeared to be on his way to Corinthians until the proposed move fell through this week. The transfer would have reunited Tevez with his former club, but Corinthians said they needed more time to arrange a deal.
Tevez has been a stabilizing force up front in his time with City, scoring 43 goals in Premiership play over the past two campaigns. He had 20 goals last season in helping Manchester City qualify for the Champions League.
While his departure would be a blow to Manchester City, the club is exploring avenues of improving its squad through the acquisition of multiple players, according to Mancini, who wouldn't mention specific names.
The club has been linked to highly sought-after striker Sergio Aguero of Atletico Madrid. But Mancini cautioned that the competitive market doesn't make it easy to sign players of Aguero's caliber.
"It's difficult to buy good players because all the good teams want these players," Mancini said. "I hope before the game against United, we can add players."
Manchester City will play the third game of its preseason tour against the host Los Angeles Galaxy of Major League Soccer on Sunday. Already Manchester City has defeated Club America and the Vancouver Whitecaps on its trip.
"The games have been good for what we need at this stage of preseason," midfielder Gareth Barry said. "The one on Sunday will probably be the toughest test. But we're where we want to be."
Tevez has been absent from the U.S. tour while playing for Argentina in Copa America. Barry said his teammates remain relatively unaffected by the uncertainty surrounding the star striker.
"Obviously, there are a few conversations about it. But the lads are just trying to get fit and enjoy the games," Barry said. "For the players, there's nothing really you can do anything about."