The Germany midfielder missed the victories over Newcastle United and Cardiff City due to a shoulder injury, but he is closing in on a return.
Wenger will take no risks with Ozil for the FA Cup third-round tie with north London rival Tottenham this weekend, but the Arsenal boss expects him to feature at Villa Park on Jan. 13.
"The specialist thinks Ozil could be ready for Saturday. It is no big damage, just the pain now," said the French manager. "I believe he will be short for Saturday and should be ready for Aston Villa."
Nicklas Bendtner has been added to Arsenal's injury list after the striker sprained his ankle in the victory over Cardiff.
The Denmark international sustained the injury as he scored the opening goal against the Welsh side on New Year's Day and Wenger revealed he will be out for "weeks".
Bendtner's contract expires at the end of the season so he is entitled to hold talks with other clubs, but Wenger is hopeful he will stay at The Emirates.
"We cannot stop him (talking to clubs) but he says he wants to stay here," he said. "If he is focused on staying with us and his job, he is a great striker."