The Italian appears to have already given up on the chance of signing the Dutch international as he believes he will not be able to leave the Gunners
The Dutch international has been in scintillating form this season and it was reported that the Italian would make an offer for him in the summer but these claims have now been rebuffed.
Mancini told talkSPORT: "I said only that we are a top team and if we want to ask about the good players, we are interested.
"[Robin] van Persie, for us, is the best player but I don’t think he can leave Arsenal."
Van Persie has scored 32 goals already this season and has one year remaining on his contract with the Gunners.
If the 28-year-old does make the move north, he will be the fifth Arsenal player to do so in recent seasons, with Samir Nasri, Gael Clichy, Kolo Toure and Emmanuel Adebayor all recently joining the Eastlands outfit.
Earlier on in the week, Mancini likened van Persie to Lionel Messi, Cristiano Ronaldo, Sergio Aguero and Mario Balotelli.