Walcott remains in a stand-off with Arsenal over a whopping £95,000-a-week, five-year deal.
But Gunners boss Wenger said: "I don't think Theo is only interested in money.
"It is very difficult to be predictable in this kind of situation. I only speak for our side and we want him to stay, we're ready to do it."
Wenger remains hopeful Walcott, 23, will commit his future to the club. But he also conceded he does not know whether the star's desire to play as a central striker will be a determining factor in negotiations.
The Frenchman added: "Will that play a part in his decision? I don't know. Only Theo can answer that question."
The Gunners are yet to hold face-to-face talks with Walcott - a dangerous policy given the England man can walk away for nothing in the summer.
Wenger said: "It will have a positive effect on the team if we manage to sign him. Our first priority is Theo."