The Dutchman has taken his form to a new level this season, but he is heading towards the final year of his contract and there are fears he could leave the club.
Talks were put on ice last year, but are set to resume at the end of the season and Wenger expects a decision to be made in the near future.
Asked about Van Persie's contract situation, Wenger said: "That will be sorted at the end of the season."
Pressed on whether a decision would be made before Euro 2012, Wenger replied: "Yes."
Van Persie is expected to be crowned PFA Player of the Year at a gala dinner on Sunday night, and Wenger feels the player is being rewarded for the way he carries himself.
He said: "Physically, Robin is good. He has a very healthy life very focused on football - he takes care of everything. That is why he manages to do that."
Meanwhile, Van Persie has laughed off reports linking him with a transfer to Barcelona and has moved to explain the source behind recent speculation.
The Arsenal captain was photographed at Barcelona's team hotel in London on Monday ahead of their Champions League semi-final first leg against Chelsea.
But the Netherlands striker has revealed his motivation for the visit was to catch up with international team-mate Ibrahim Affelay.
"The explanation is really very simple. My very good friend Ibrahim Afellay plays for Barcelona," Van Persie said in Arsenal's Official Matchday Programme ahead of their Premier League clash against Chelsea.
"After a bad long-term injury he was finally back with the team - and during his absence I had been in contact with him a lot, but I hadn't seen him. This was an opportunity for me to go and visit a close friend, show him my support and catch up.
"Unfortunately this had to be at the hotel, because he was not permitted to leave it. I was wearing my Arsenal tracksuit and we sat down by the reception to have a chat and some food - everyone could see us and there was nothing to hide. I can't imagine anyone conducting transfer negotiations in these circumstances!
"The visit to the hotel was a social one and had nothing to do with the future of my career. I do have a social life next to football, even if my wife tells me that it sometimes doesn't seem that way! Nothing has changed in the sense that my intention remains to discuss my future in the summer."