The Netherlands forward has reportedly attracted the interest of Manchester City and Juventus, but his manager insists it is vital he stays with the Gunners this summer
Van Persie is a reported target for Manchester City and Italian giants Juventus following a season in which he scored 30 Premier League goals in 38 appearances.
And the Frenchman expressed his hope that the 28-year-old will repay the faith shown by The Gunners during several injury absences by committing his future.
In his blog for Eurosport, Wenger wrote: "We want to keep Robin van Persie at all costs, because we depend on him offensively.
"I have always supported him even in the hardest times, and I hope he will end his career at Arsenal."
Wenger also went on to discuss his most recent signing, France international Olivier Giroud, who has arrived from Montpellier for a fee of around £13 million.
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"I have known Olivier Giroud for some time,” Wenger continued.
"The first time I saw him, I found he had something intelligent and dangerous. I always said he could score goals and assist his partners.
"Our game is based on cooperation between the players in the offensive phase and he will integrate easily. I don't like simple goalscorers, they must also add to the collective.
"He is good in the air which is rare. He is quite complete and has a great room for improvement."