Van Persie, who will celebrate his 29th birthday on Monday, has told Arsenal he will not sign a new contract leading to a three-way battle for his signature between City, United and Serie A champions Juventus.
Juve have already suggested that Van Persie is out of their reach, and with Mancini also distancing himself from a deal for the Netherlands international it could be that, as reported by the British press on Sunday, he will sign for United this week for a fee in the region of £20 million.
When asked about a move for Van Persie, Mancini told Sky Sport Italia: "Van Persie? No, I don't think he will come here."
Lucas Moura is tipped to join Shinji Kagawa and Nick Powell as United's summer signings, and if Van Persie arrives too boss Sir Alex Ferguson will consider it a productive summer in the transfer market.
Sir Alex did not travel with the United squad for the pre-season match against Valerenga on Sunday, suggesting he was keen to stay at home and finalise transfers. He has always been keen to add the personal touch to make sure he gets his targets.
Mancini also said it was unlikely striker Edin Dzeko would get his wish of a move away from the club, who has been linked with Juve himself.
"I'm pleased, as this means we have good players, but it's pretty unlikely he will leave," said Mancini. "He is right to say it's no fun being on the bench, but when you join a big club then competition is normal."