The Dutchman has only one year left to run on his current deal at the Gunners and has yet to agree a new contract at the Emirates.
Van Persie has been targeted by both Juventus and Manchester City, with rumours suggesting a fee of around £30million should be enough to force Arsenal's hand.
But speaking to Corriere Dello Sport, Wenger claimed those reports are wide of the mark and that the 28-year-old will stay in north London.
"I am certain that Robin will remain with us," he said. "If you want to know why I am so certain Robin will remain with us, it is because there is no reason in this world why a great player like Van Persie should go and play for you, in Italy and in your competition.
"Your football (Serie A) is at an inferior level to the Premier League."