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.
Van Persie, 28, plundered some 37 goals in all competition to help fire Arsenal back into the third place in the Barclays Premier League - and with it automatic qualification into the Champions League once again.
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."
Arsenal are keen to show their intent for next season with more signings to follow German striker Lukas Podolski.
A £13million move for France forward Olivier Giroud is, according to Montpellier's officials, at an advanced stage.
Signing the 25-year-old, who scored 25 goals last season to help Montpellier win the Ligue 1 title, would be likely to lead to some of Arsenal's fringe players being sold - including Denmark striker Nicklas Bendtner and Morocco international Marouane Chamakh as well as Mexico forward Carlos Vela and Brazilian midfielder Denilson.