Walcott, the club's top scorer this season, is speculated to want around £100,000 a week to move closer to the pay deals of fellow England internationals, as well as opportunities to prove his worth up front.
The Gunners confirmed new long-term deals yesterday with five of their young stars on Wednesday afternoon, as exclusively revealed by Goal.com and Wenger now wants Walcott to follow suit by penning fresh terms.
Wenger told reporters: "We will not sell Theo in January. That is for sure.
"He has to make his mind up now and I hope the decision taken by the other players will help him to do that.
"My gut feeling is that he belongs to this club and that I hope he will do it and sign for us. I have always been convinced he will stay.
"But it is not imminent, it is not as far as that. We know that once he's made up his mind it will be quick."
When quizzed on whether the pay packet Walcott is seeking would be a fair reflection on the player and his progress, Wenger was less certain.
He said: "I never see football like that. You never fix yourself a limit on financial restrictions.
"The question, at the end of the day, is can you pay what the player wants? And does it fit with your wage structure?
"I always fought in my life for players to make money so therefore I am happy when the players make big money. I did always fight for that but it has to be made possible for the club to pay it.
"But I believe the board will follow my recommendation if it is possible. We have a wage bill that has to be respected.
"When we go overboard and higher than it is expected, I ask the board to do it most of the time they follow my demands."