The 25-year-old - who is in the final year of his contract at the Emirates Stadium - has been plagued by injuries in recent years, including a broken leg in April which brought a premature end to his loan spell at Bournemouth.
Wilshere had enjoyed his most consistent spell of first-team football since 2010-11 during his time at the Vitality Stadium, though, and recently claimed to be in the best shape of his career as he continues his recovery.
"Wilshere struggled historically with repeated injuries. Nobody would question his talent. Nobody would question his exceptional ability to beat people with the ball. But in this job you need first health. Today the requests and demands in the competitions are so high physically that you can only be your best physically if you can play at least 10 games on the trot," Wenger told beIN Sports.
"That is what's at stake for Jack Wilshere. Keep health and compete and be capable to compete. If he can play from now until December at the top level he will be back. If there are other setbacks then it will be difficult for him. It's a vital season, it's the end of his contract, a World Cup year. He's an Arsenal player since he's a kid so all that is at stake for him.
"You would love a player like him, of that quality, to come back. In fact he had a very good game in BATE Borisov, a very brilliant first half when he was back to his best. So he's not far away now. But let's hope in the next two to three weeks he can play regularly in the first team."
Wilshere has made three appearances for Arsenal so far this season - one in the EFL Cup and two in the Europa League.