The England international's career in North London has stagnated over the past couple of years, leading to a season-long loan move to Bournemouth last time out.
Wilshere failed to truly light up the Vitality Stadium and frustratingly picked up a fresh injury late in the season when breaking his leg, which delayed his return to training.
Wenger refused to confirm whether the 25-year-old will start against FC Koln in the Europa League on Thursday night, but he has challenged the midfielder to now get his career back on track at Arsenal.
"There was always a huge pressure on him to come back as quickly as possible and to expect a lot," he told reporters. "He's on a good way in training. He's getting stronger and stronger every day, and that's what we want from him.
"He was injured at the start of the season from last season, so he was a bit behind the other players but he's getting better and better. Every game is an opportunity for him and this season's a good opportunity for him as well."
Wilshere appeared 29 times in all competitions in 2016-17, including twice for Arsenal prior to being sent out on loan.