The 18-year-old, who signed for Arsenal from Southampton this summer, has scored four goals in two starts for the Premier League side this season.
Despite his impressive start, Wenger has said that England shouldn't be "too quick" to snap up the youngster.
"I don't rule him out of Euro 2012, and it depends on his progress," ESPN quotes the Frenchman as saying. "I think sometimes you pick too quick in England, but you cannot rule him out because he has the basic talent.
"It will depend on the next five, six months how much he will adjust to the physical intensity of the game."
The Gunners take on Sunderland at the Emirates on Sunday.