The Portuguese star played alongside the Argentine during his Old Trafford days, but Tevez could be on his way out of City this season having asked for a move.
United and City come up against each other in Sunday's FA Community Shield, the season-opener at Wembley, and Nani has reminded City boss Mancini of Tevez's talent.
"I played with Carlos and he is an important player for any club," he told The Sun.
"I don't know if he will stay at City but, if he does go, it will be a big problem for Mancini because of the way that he plays and his experience.
"The Community Shield is the first official title of the season and we want to win. And facing City makes the match more exciting.
"It's also our first derby of the season, so to lift the trophy would raise our morale and inflict pain on our rivals."
This summer, Nani has reportedly been the subject of interest from Serie A giants Juventus, who believe the 24-year-old is unsettled by the ?17million arrival of fellow winger Ashley Young.
Nani insists that is not the case, though, and has vowed to continue working hard for United's cause.
"I prefer to forget the rumours about other clubs being interested in me," he added. "I don't want to say too much but, if they are true, it's because I have been working well.
"But, sincerely, I am focused only on United.
"I speak with Mr Ferguson a lot - many times - and he is always very clear. He explains what he wants from me and I do everything to try and fulfil the mission."
Source: Team Talk
Source: Team Talk