The Italian boss recently admitted that he had held talks with several other clubs during the summer, including Ligue 2 outfit Monaco.
But, despite speculation over Mancini's future increasing following City's mixed start to the season, Vieira says that the Premier League champions are keen to retain his services.
"He signed a five-year contract and I think that shows the commitment between himself and the football club," the 36-year-old told reporters.
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"[Speculation] is a part of the game," he added to BBC Radio Manchester. "You people, the journalists, try to find the little things that will sell more papers or get more people listening to the news. We accept it, no problem at all.
"Since he [Mancini] has been at this football club, his record has been fantastic. You don't win the FA Cup or the Premier League with an average manager. You have to be good.
"Everybody says we have a good team, but you have to manage 25 players. A lot of credit must go to Mancini because he has worked hard to bring silverware to the football club."
Vieira also refused to accept that the club's Champions League campaign is yet over but admits that City have a lot to learn at such an elite level.
"Of course we didn't help ourselves and do ourselves any favours, but the door is not completely closed," added the former France international.
"It is going to be difficult and not many people believe we can go through, but we have to believe.
"The Champions League is a different level and it's new for us. We're learning and I believe we're going to get better, but it will take time."