The 20-year-old has not featured for the Gunners at all this season because of a stress fracture of his right ankle, which at one stage looked likely to rule him out for the whole campaign, including England duty at Euro 2012.
However, the outlook on his recovery has recently improved, and Wenger told the club's official website: "If all goes well, he will be back with the squad in three weeks. If he has no setbacks he will play this season.
"Wilshere is back with the ball and for us that is a huge step. The work we do with the ball is always quite demanding."
In Wilshere's absence, Arsenal are 7/1 with Paddy Power to beat Aston Villa 2-1 in the Premier League on Saturday.
The Gunners boss was also optimistic regarding the young midfielder's chances of featuring for England in Poland and Ukraine this summer.
"That’s a decision fortunately I don’t have to make," the Frenchman continued.
"I will only intervene if I believe medically he is at risk.
|"He is an England player and if he has played some games before the end of the season it is a possibility"
- Wenger on Wilshere's chances of making Euro 2012
"He is an England player and if he has played some games before the end of the season it is a possibility [for him to go to Euro 2012]. If he has not played at all before the end of the season I don’t think it’s realistic.
"The next three weeks will decide how well he progresses. We have gone for a very cautious attitude with him. We will not force him into training with any pain. So we might have to be slower than expected. If all goes well he will be back in full training in three weeks. But that is not sure yet."
Wenger was, however, less enthusiastic about the possibility of Wilshere representing Team GB at the London Olympics, cautioning: "The Olympics destroys the start of season for us.
"If Wilshere could play I would rather he went to the Euros than the Olympics. It depends how well he will develop."
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