Van Persie has been linked with a move away from Arsenal for much of the summer after releasing a statement revealing that he would not sign a new contract in north London.
City have been among the chasing pack to sign the Dutch striker, alongside Manchester United and Juventus.
Mancini told Italian television: "Van Persie? No, I don't think he will come here."
One of the longest running transfer sagas of the summer is far from over, but recent reports have said that van Persie is impressed with Arsenal's recent transfer business.