Mancini saw the 21-year-old in action during Celtic's 3-0 UEFA Champions League loss to Juventus on Tuesday.
But the City boss rubbished suggestions that a move could be on the cards in his press conference ahead of Saturday's FA Cup tie with Leeds.
The Italian said: "I saw him for the first time against Juventus, I never saw him before.
"But every time I go to see a game, the next day people say 'Manchester City want to buy this player'."
When asked whether he would be interested in signing Wanyama, Mancini added: "At the moment, no. I think he is a good player."
The Kenyan joined Celtic in 2011 from Belgian side Beerschot AC. He has scored 12 goals in 79 appearances for the SPL champions.