Wilshere was hoping to be back in action by February, but he could defy all the odds and play his first game by the end of January.
Wenger said: "The most important thing for Jack Wilshere is that he gets fit again. The positive news for us and England is that he is progressing very quickly.
"I would keep February. Jack pushes every day of course to be quicker than the medical expectations. He might win the battle."