Walcott's current contract with the Gunners runs out in June 2013 and he has yet to commit himself to the London club beyond that period.
Wenger, though, is trying to persuade the 23-year-old to continue to ply his trade at the Emirates.
"We are still trying to extend his deal," the Frenchman is quoted as saying by The Sun.
"When a player doesn't want to stay, you either force him or you let him go."
Arsenal will begin their Premier League campaign with a home game against Sunderland on Saturday.