Gunners boss is hoping that his side can seal their entry into the Champions League group stages and boost their chances of holding onto their leading striker
The Dutchman is set to claim the league’s Golden Boot after a stunning campaign which has seen him net 30 league goals.
This form has seen him linked with moves away from the Emirates Stadium, but Wenger is optimistic that a third-place finish could convince him to stay.
Asked if Van Persie would remain at the club, the Frenchman told the press: "On my side I am inclined to think, 'yes'. But you should ask him. I don't know whether it will have an influence on him.
"Anyway, we don't focus on just that. Robin is not at the end of his contract."
The sales of Cesc Fabregas and Samir Nasri last summer were heavily criticised, but Wenger does not believe that the club will be forced to sell again.
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"People speak like our position is not important. Our position is very important," said the Gunners boss.
"Our position with Cesc was to let him go because he wanted to go."
Arsenal have already begun strengthening ahead of next season with the £10 million signing of Lukas Podolski. However, Wenger believes that the return of some of his current players, who have been sidelined with long-term injuries, will be just as important.
"Another way to strengthen for us is to get [back Jack] Wilshere and [Abou] Diaby, who didn't play at all the whole season," said the veteran manager.
"You look at the number of players - we have 34 players when they all come back. That means you have to pay nine not to play."