Van Persie only has 12 months remaining on his contract and Wenger had previously been hoping to resolve his captain's future before Euro 2012.
An agreement was not reached before Van Persie headed off on Netherlands duty, however, and there is continued speculation that he will leave Emirates Stadium this summer.
Premier League champions Manchester City have been linked with last season's top scorer, but the 28-year-old's father recently stated it is 'impossible' for him to join one of Arsenal's domestic rivals.
Spanish giants Barcelona and Real Madrid have also been mooted as admirers of Van Persie, but reports have claimed Juventus hold the strongest interest in the player.
The Serie A champions are aiming to sign a high-profile striker ahead of next season, but Wenger does not expect Van Persie to head to Italy.
"He will stay at Arsenal," Wenger told the Italian newspaper La Repubblica.
"There is no reason why a top player, a big champion would want a move to Serie A - in terms of the prestige of the league, the level of play or financial considerations.
"If he moves there, I will buy you a caramello."
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