The Frenchman was booed by his own set of supporters against Manchester United last weekend for substituting the youngster after an impressive first league start for the club.
But he has hailed the progress the former Southampton starlet has made since moving to the Emirates Stadium in the summer and has backed him to challenge for a Three Lions spot ahead of the tournament.
"You cannot rule it out and it is not because you are young that you cannot play. We will see in the next three months and if he does well, why not?" Wenger told reporters.
"We live in a world of immediacy. I would not have expected him to be so mature in September because he still looked like a boy. Now suddenly he looks like he can take pressure and that he has the personality to produce under pressure.
"But he has only really played one game at the top, so let's see how well he does."
The Gunners boss also said the club's faith in youngsters proved a factor in Oxlade-Chamberlain's decision to move to the Emirates.
He said: "I believe that when Oxlade-Chamberlain was making his choices, he knew that he would have a chance here.
"I think we have always shown we are willing to take out experienced players and put younger ones in when they deserve it."
He added: "They get a chance here that is for sure.
"Young players want to join us because they know they will get a chance at the top level.
"I believe for an English national team player, you have to start to play at 18 at the top level if you want to become an international player. They all played at 18 - John Terry, Rio Ferdinand, Wayne Rooney, Steven Gerrard."
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