Oxlade-Chamberlain, 18, has impressed on his four appearances for the Gunners this season following his £12 million summer move from Southampton, scoring against Shrewsbury in the Carling Cup and Olympiakos in the Champions League.
Despite his rapid progress, the youngster is determined to take things one step at a time.
Oxlade-Chamberlain told Arsenal Player: "It is a work in progress and I don't think there's any need to rush into things. I trust the boss and he is going to develop me.
"I knew that when I signed here it would be hard for me and that maybe in my first season I wouldn't get a lot of game time, but I'm learning so much in training from the likes of Robin van Persie and the rest of the boys - and the manager as well.
"I have only had a few appearances, but I have scored two goals and I am happy with that."
Oxlade-Chamberlain added: "I think there's a lot more to come from me so I am just going to keep working hard, keep learning in training. It is down to me, I have got to put pressure on the boss to select me.
"I can only do that by training well and, when I do get my chance, impress him. The boss has said it is up to me, he is going to work with me the same way I have to with him."
Oxlade-Chamberlain is set to feature for the England Under-21 side at Colchester in Thursday night's European Championship Group 8 qualifier with Iceland, against whom he smashed a hat-trick in Reykjavik last month.
England have won all three of their qualifying matches to lead the group as they look to reach the 2013 finals in Israel, and Oxlade-Chamberlain believes Stuart Pearce's squad are bonding well.
"If you do get on with (your team-mates) it makes it a lot easier to play, train and work hard together," he said. "The new team that's being put together is really good - we have a lot of youth mixed with the older heads."