Wilshere, 20, has yet to feature for Arsenal this season after undergoing surgery on an ankle injury he aggravated during last summer's Emirates Cup.
The midfielder looked to be closing in on a return only to suffer a setback, but he has recently been making steady progress in his recovery.
Gunners manager Wenger said: "We try to keep the hope alive for him and without taking too many risks.
"That means we adapt day to day, to manage him, to improve his physical state and get him fit as quickly as we can without taking too big a risk, which means when he has pain we stop him.''
On the prospect of Wilshere being involved for England in the summer, Wenger added: "To go to a big competition without having played at all is impossible.
"In the next four or five weeks we will know more and the next three weeks will be decisive. You would think a player who wants to play in June will have to be competitive at the end of April. The next three weeks will decide [if he can go to the Euros]."