The England international’s contract expires next summer but the Gunners are yet to tie the winger down to a long-term deal at the Emirates.
Walcott has been in good form this season and is the Gunners’s leading marksman, scoring eight goals in all competitions.
Wenger insists that the will "do the maximum" to keep the player, who recently claimed he deserved an extended run in the first-team, at the Emirates.
He told the club’s official website: "My desire is to keep Theo. We do what’s needed to keep him and hopefully [as] I told you many times, we can sort this situation out very soon.
"Very soon is before the end of December - one way or another, that is for sure.
"I don’t want to go into any details but you can believe me [that] we do the maximum we can to keep our best players."