The 28-year-old Dutchman, who has scored 32 goals in all competitions this term, said last month he was putting contract talks on hold until the end of the season.
With Arsenal destined to finish without a trophy for a seventh successive year and facing a battle to seal a Champions League spot, Premier League leaders City could pounce to reunite Van Persie with former Gunners trio Samir Nasri, Kolo Toure and Gael Clichy.
"I think if there is a good player who wants to leave a club, then we are interested," Mancini was quoted by British media as saying.
"I think all the good teams are interested in Van Persie.
"At the moment, Van Persie is one of the best strikers in Europe with Lionel Messi, Cristiano Ronaldo and with Sergio Aguero and Mario Balotelli. He is a fantastic striker but I think he will remain with Arsenal."
Abu Dhabi-backed City are likely to be able to offer wages higher than anything Arsenal usually pay and in their current form, look more likely contenders for silverware than the north London team.
Mancini said he expected Arsenal to bring in some top players before next season to enable them to mount a bigger challenge, which could be enough to persuade Van Persie to stay put.
"He is Arsenal's best player at the moment and it is difficult for them to give him to another club. In the summer I think Arsenal will buy good players," the Italian said.
"I think because Arsenal is a top team, they want to win the next Premier League, so for these reasons [they will do everything to keep Van Persie]. I don't think he will be cheap just because he has one year left on his contract."
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