Wilshere is yet to feature this season for the Gunners after requiring surgery on his ankle. Initially tipped to return in February, a series of setbacks have seen his return date delayed until closer to May.
The England international is hoping to get picked for Euro 2012 and will need to prove his fitness ahead of the tournament. And Wenger admits there is a chance the 20-year-old could do so.
"The last scan was good and he can start to jog again so he is on the way back - but we have to be very cautious with him," Wenger said. "I hope to have him back before the end of the season, but we go step by step."
Arsenal's more pressing priority is a Champions League last-16 second leg on Tuesday against AC Milan, who hold a daunting 4-0 advantage. The Gunners have shown their comeback abilities in recent weeks, bouncing back from a goal down at Anfield and a two-goal deficit against Tottenham, so Wenger is ready to unleash his troops on the Italians come Tuesday.
"At the first look, it appears impossible," Wenger said. "But you have to have a real go and play with belief and think you can do it. We want to make the impossible possible - that is basically our target.
"You never know in the game. We have nothing to lose. Maybe I will change individuals in the team and go for it and see if we can put them under pressure and try to score goals."
Key to Arsenal's hopes is Robin van Persie, the two-goal match-winner at Liverpool. But Wenger is keen not to heap too much pressure on the Dutchman to score against Milan.
"I just do not want him to play with too much pressure," Wenger said. "I just want him to enjoy the game and I feel as long as the theory of scoring is not interrupted, the confidence of the player is high and he scores naturally.
"Once you do not score in two or three games you become a little bit more edgy. So the best thing is for him to score goals."