Walcott scored twice for the Gunners in a in a 6-1 rout over Coventry City in the Capital One Cup with a pair of impressive strikes.
Wenger confirmed that he is desperate for Walcott to stay even if he cannot guarantee him a place in his preferred central position.
The Gunners boss said at the post-match press conference: "I am not against [him playing up front]. We will try, at the moment there is a big competition up front.
"He is a great finisher now. His time will come. "I want him to stay. I always said I wanted to sign him and extend his contract."
Walcott revealed earlier this week that he has yet to sign a new contract at the Emirates because he wants assurances that he will get a chance as a striker.