The Netherlands international announced in July that he would not be signing a new contract at the club, which had fuelled interest from Manchester United and Juventus, in addition to City.
However, a move to the Premier League champions now appears unlikely, with Mancini revealing his pessimism over a possible move.
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"I don't think Robin van Persie can come to City,” the Italian told Sky24.
Van Persie won last season's Professional Footballers' Assocation Player of the Year award as he scored 30 Premier League goals and led the Gunners to third place and Champions League qualification.
In his statement announcing his intention not to extend his contract, which expires next summer, the forward voiced his desire to move to a more ambitious club, with the Gunners having last won a trophy in 2005.
However, his mood was believed to be vastly improved after the club moved close to signing Malaga's Spain international attacker Santi Cazorla and launched a move for Real Madrid playmaker Nuri Sahin, alongside the earlier additions of forwards Olivier Giroud and Lukas Podolski.