Oxlade-Chamberlain joined Arsenal for a reported fee of £10 million in August, and has gone on to score twice in two starts for the Gunners, including one in the Champions League. It has been an impressive acclimatisation by the youngster, considering he was playing in League One for Southampton last season.
With Wayne Rooney ruled out of the first three matches of Euro 2012, there is a vacancy in England's attack - and Wenger suggests Oxlade-Chamberlain, already an Under-21 international, could be the man to step into the void.
"I don't rule him out of Euro 2012, and it depends on his progress," Wenger said. "I think sometimes you pick too quick in England, but you cannot rule him out because he has the basic talent. It will depend in the next five, six months how much he will adjust to the physical intensity of the game.
"I didn't expect to be as comfortable so quickly, of course he has done extremely well. He still needs more time to adapt to the intensity and level of games, but he has the quality already for top-level Premier League games."
However, Wenger did suggest that England boss Fabio Capello should select Rooney for next summer's tournament in Poland and Ukraine. "I am not in position to tell Fabio Capello what to do," he said. "If you ask my opinion, it means he should go to the European Championship. If you expect your team to win, you have to take your best players."
Wenger insists Rooney's punishment was harsh but understands why UEFA have made an example of the star. He also urged the Football Association not to appeal against the length of the ban.
"I have experienced myself that UEFA can be very harsh. You have to accept it,'' Wenger said. "The FA has to make a decision on the appeal knowing that they can be punished more. The maximum they can gain is one game but they risk getting one game more so maybe it would be wise not to do anything.''
Wenger, however, believes critics should not be too hard on Rooney.
Wenger added: "He is a great player. The other day he had a bad reaction. I've seen that from (Zinedine) Zidane and many great players. It's sometimes a consequence of the immense pressure they are under, everybody expects them always to do something special.
"On the day he knows that he had not a special day because recently he was exceptional in every single game and on the day he was not in such good form and he was frustrated.
"He shouldn't have done it but you cannot have the commitment of Rooney and as well not expect that in one game he can go a little bit overboard. He is a guy who fights in every single game.''