Along with local rivals United and Italian giants Juventus, City are one of the clubs interested in Van Persie, who last month announced he would not be signing a new contract with Arsenal.
However, the prospects of the Holland international, who turns 29 on Monday, joining the Premier League champions now look remote with Mancini admitting he does not expect to have the player in his ranks next season.
The Italian was quoted as saying by various newspapers: "Van Persie? No, I don't think he will come here."
Van Persie's existing deal at Emirates Stadium expires next summer but Gunners manager Arsene Wenger is desperate for the prolific hitman, who enjoyed a stunning campaign last season, to remain at the club.
Van Persie won both Professional Footballers' Association and Football Writers' Association player of the year prizes in recognition of his 36-goal contribution for Arsenal in the 2011/12 season.
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