Wenger deployed Walcott in the player's preferred central attacking role tonight, and felt it was an "encouraging" display.
The Arsenal manager is hopeful an agreement can be reached sooner rather than later.
The Frenchman said: "It is not my decision, it is Theo's decision as well - if it is [only] my decision, it is quickly done.
"I hope that when he considers his future he will think this is the best place for him and sign for us.
"I will just say our desire and will is clear, and Theo knows that. Hopefully we can get to a happy end with it."