Wilshere, 20, has spent the entire season on the sidelines after undergoing surgery on his injured ankle last September. The midfielder has yet to train with the first team and is still confined to training by himself in the gym.
Arsenal have five games remaining this season but Wenger remains cautious over whether Wilshere will play any part, and he said: "I will not take any risks with him. He is making slow progress so we still have to monitor the situation a little bit at the moment."
He added: "We are now in mid-April, the Euros start in the middle of June. Jack has not played for the whole season and anyone who knows what is required at the top level, in terms of intensity, it's getting short now."
When asked if Wilshere's spirits were high, Wenger added: "How can you be at 19 years of age when you're only dream is to play football. He's down. Jack is mentally strong. But what is holding him back is that he can't play football, so he can't be happy."
Meanwhile, Wenger wants referees to be allowed to stop the game to consult video technology to make decisions in the Premier League.
Wenger's call comes after a week of high-profile mistakes by match officials which saw two offside goals awarded to Chelsea against Wigan last Saturday and Manchester United deprived of a clear penalty for handball against Wigan on Wednesday.
Wenger said: "Last weekend was a very, very bad weekend. The football authorities on a global scale have to sit together and see how we can improve.
"There are some immediate decisions to make but as well it is time for us to help the referees. To all be united and have a less conservative approach and finally opt for video.
"Video will help the referees. Not question their authority. It will give them more credit, more authority and less mistakes. (We need) instant video replays on the demand of the referee."