The French boss has stated that the winger looks keen to remain at the Emirates Stadium.
The England international has gone through a tough 12 months, with injuries blighting his chances to play for the North London club.
Upon his return to fitness, Walcott has found first-team opportunities hard to come by, with the likes of Mesut Ozil, Danny Welbeck and Alexis Sanchez getting the nod in attacking midfield roles.
The former Southampton prodigy’s contract is starting to run down, with it remaining unclear where he will play his football in the future.
Despite the uncertainty, Wenger has given a hint that he feels Walcott will remain at the Emirates Stadium.
“We are already talking to him,” The Guardian quote Wenger as saying.
“Today I’m not in that mode of thinking [about Walcott’s possible departure] because I just think I want him to stay.
“When you go into negotiations with a player it is with a desire for him to stay. He looks keen to do it and I am keen to do it, so let’s see what comes out.”
Arsenal are in action against Swansea on Monday night, with Wenger’s men hoping to finish second in the Premier League this season and still having a chance of retaining the FA Cup.