The current Premier League champions are yet to sign anybody this summer, and their inaction to date continues to frustrate Mancini as he looks to build a lasting legacy at the club while turning them into the English game's dominant force.
The Italian boss has now admitted that the club's chase for the Dutch forward is all but over, arguing that he is either destined to stay put at the Emirates or move to the club's bitter rivals Manchester United instead.
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"Van Persie is not our player. He is an Arsenal or United player," Mancini told reporters.
"These questions you should ask other people. I don't know what I can say. After three or four months... nothing.
"I think when you win something you should look to improve and buy new players, but not too close to the end. The league was finished in May and I think now it is very difficult to move in the market.
"But I don’t want to talk any more about players, my thoughts are now with the game against Chelsea. Now I have to think about the game."
When pressed further on whether he was happy with the way that business was conducted with concerns to transfer at the club and the role that Marwood plays in negotiations, Mancini didn't pull any punches.
"You should talk to Brian Marwood for this. Not me. Talk to Marwood please," he added.
"No I'm not happy. I don't want to say anything at the moment. For me we have a good team. But we need to continue to improve."