The England international midfielder has not featured for The Gunners this season as yet due to an ankle injury, and suffered a setback before Christmas as his rehabilitation looked to be nearing an end.
However the French coach is looking to have his talisman back available before the end of the season, but won’t rush his recovery.
“Jack can be back within a month if all goes well,” Wenger told Sky Sports.
“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,” he stated.
Meanwhile, Arsenal take on AC Milan at the San Siro on Wednesday night, and the Emirates Stadium manager has admitted to studying Tottenham’s victory over the Italian giants from last season in preparation for the game.
“I have seen [that game], yes. Milan had a lot of the ball and Tottenham caught them on the break at the end of the game,” he told the club’s official website.
“You never decide when you break, you break when you can. It was a game which was vastly dominated, especially in the second half, by Milan.
“We will not decide at the start of the game that we will sit in our half if we have to, like Tottenham did. We will do it and then try to catch them on the break.
“But at the start we will try to get out of our own half and try to get up there and play. Spurs won the game when they were dominated, but that is football today,” he stated.
By Gareth McKnight