The 20-year-old has not featured for the Gunners this term after suffering an ankle injury during pre-season and having to undergo surgery.
Wilshere then suffered a fresh setback earlier this month when it was confirmed he had developed a stress fracture during his recovery, sparking fears the England youngster would be ruled out for the season.
But Wenger has reassured Arsenal fans that his recovery is on track and the Frenchman is certain he will return before the end of the season.
“Jack can be back within a month if all goes well,” said Wenger. “The recovery of his latest problems looks very good. The latest scan was very positive.
“We go cautiously step-by-step because we tried to push him back quicker in the first instance and he had a setback. So this time we have to be cautious and not go too quick. He can be back before then end of the season, of course.”
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