A stress fracture to his right ankle has prevented Wilshere from playing this season but Wenger revealed that he may return to action in five weeks. If the final stages of his rehabilitation go well, he could participate in Arsenal's last three Barclays Premier League outings against Stoke, Norwich and West Brom.
That would enable him to travel with England to Poland and Ukraine, although Wenger would object if he deemed it to be risky for the 20-year-old, and he said: "Wilshere going to the Euros is a decision that fortunately I don't have to make. I would only intervene if I believe that medically he's at risk."
He added: "As an English player, if he's played some games before the end of the season, it's a possibility. If he has not played at all before the end of the season, I don't think it would be realistic.
"The next three weeks will decide what happens. We'll see how well he progresses. We've taken a very cautious approach with him. We'll not force him into training with any pain, so it might have to be slower than expected.
"In three weeks he can be back with the squad - if all goes well - and then another two weeks to get fully fit.
"We don't have to hold him back at the moment because he suffers a lot for fitness. After three weeks we'll have to hold him back
"I think he will play this season if he has no setback now. His last scan was positive so he should play."
Wenger is adamant that he does not want Wilshere representing Great Britain at the Olympics.
"The Olympics destroys the start of the season for us. If he could play, we'd rather he went to the Euros than the Olympics," he said.