The 28-year-old will be out of contract at the Emirates Stadium in the summer of 2013, and questions have been frequently raised over his long-term future after the striker revealed he would not open negotiations over a new deal until the end of the current campaign.
Arsenal's barren spell without a trophy looks set to run into a seventh consecutive season, and is believed to be the main reason why Van Persie is considering his options.
With 32 goals already to his name this campaign, there will be no shortage of admirers of the Holland international, should he make his desire to leave Arsenal public, but Mancini doesn't think that will happen.
"I think Van Persie at this moment is one of the best strikers in Europe with [Lionel] Messi, [Cristiano] Ronaldo and with Sergio [Aguero] and Mario [Balotelli].
"I think he is a fantastic striker, but I think he will remain with Arsenal."
City have built something of a reputation for signing want-away Arsenal stars after securing the signature of Samir Nasri and Gael Clichy last summer, adding to the previous acquisitions of Kolo Toure and Emmanuel Adebayor, who also favoured switches to the Etihad Stadium.
"I think if there is a good player who wants to leave a club, then we are interested," Mancini continued. "But if this player wants to stay, we don't have any problem. In my opinion, Van Persie will stay at Arsenal.
"I think Robin van Persie will sign a new contract with Arsenal because if Arsenal lose also Van Persie, they will have a big problem.
"I think Arsenal will buy good players in the summer. Arsenal is a top team. They want to win the next Premier League, so for these reasons I think he will stay."