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.
Support the USA national team with an official 2013 Centennial soccer jersey from Nike. Its Official.
England will debut their new away jersey against Brazil at the Maracana Stadium on Sunday. Get in the Gear
Germany is one of the top teams ever and they will play the US on Sunday.
The hoop soccer jersey is classic and cool. The USA hooped jersey is perfect for every fan. Get in the Gear.
Manchester City will try and win back the Premier League title with this new soccer jersey from Nike!
The Nike Hypervenom is the latest cleat silo from Nike. It will change your game and is worn by the game's top players.
Jamaica is in need of a win against the U.S. Get the jersey of the Reggae Boyz.
Barcelona will wear this new home soccer jersey next season. They also have a new away jersey. Get them both.
Neymar's move from Santos to Barcelona is no doubt the biggest summer transfer.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.