The all-action performance of the 18-year-old - signed from Southampton in a £12million deal last summer - was one of few positives for the Gunners after their 2-1 defeat to Manchester United.
Oxlade-Chamberlain, whose substitution last weekend caused frustration among some of the Emirates Stadium fans, has shrugged off a calf problem and is expected to again be in the thick of the action against Aston Villa in Sunday's FA Cup fourth-round tie.
Wenger sees no reason why with more games under his belt, the powerful attacking midfielder, who has already played in the Champions League, should not follow team-mate Theo Walcott into contention for Fabio Capello's squad in Poland and Ukraine.
"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?" said Wenger.
"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."
Wenger had long been criticised for packing his side with overseas talent, but now the likes of Jack Wilshere, Walcott, Kieran Gibbs, Carl Jenkinson and Oxlade-Chamberlain all, when fit, compete for regular first-team action.
"They get a chance here that is for sure," Wenger said.
"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."
Wenger continued: "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."