Van Persie has yet to resolve his long-term future, with a year left to run on his current Gunners contract.
The Dutchman held preliminary talks with Arsenal before he left for what turned out to be a disappointing European Championship campaign as the Netherlands failed to progress past the group stages after three defeats.
Wenger, though, insists speculation of a big-money move away from Emirates Stadium, with English champions Manchester City also reported to be preparing a lucrative offer as well as the Serie A winners, are all wide of the mark.
Quotes in Italian newspaper Corriere Dello Sport, Wenger said: "I am certain that Robin will remain with us.
"If you want to know why I am so certain is that Robin will remain with us 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."