Walcott has never been known for his goals but is pushing Wenger for a chance up front this season if Arsenal get short on forwards.
He said: "I would like to put it out there that I would like to play up front.
"The boss has always promised me I will get a chance to play up front.
"It's been six years and if I just keep on scoring and doing well, I'll maybe get a chance up front with Robin.
"I'm not demanding anything, but I'm giving the boss something to think about."