Van Persie's contract with Arsenal expires in 2013 and a number of clubs have been alerted to the possibility of a shock summer move because he has ruled out discussing his future until then.
Despite his interest in the Dutchman, who has scored an impressive 32 goals already this season, Mancini believes Arsenal will move quickly to make sure he accepts a new deal.
Quoted in several national newspapers, the Italian said: "We are interested in all good players. This is normal, but not only us. I think all the good teams are interested in Van Persie.
"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 signed several Arsenal players in recent years, acquiring Samir Nasri last summer and also signing Gael Clichy, Kolo Toure and Emmanuel Adebayor.
Mancini added: "I think if there is a good player who wants to leave a club, then we are interested.
"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."
Source: AFP
Source: AFP