The player's current contract expires next summer and if no deal can be brokered before January, Walcott would be able to negotiate a potentially lucrative pre-contract agreement with a foreign club or just hold firm and walk away on a Bosman free.
"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," said Wenger.
On Walcott, he added: "I don't want to go into any details [over wage negotiations], but you can believe me [that] we do the maximum we can to keep our best players."
Wenger, though, has no concerns over a player tactical revolt.
"I don't find many players who don't want to play central," he said.
"Podolski has 101 caps in Germany, and 101 on the left. I brought him as well with the idea that, when needed, he would play through the middle.
"I like the idea, but we will use him where he is useful for the team."