Oxlade-Chamberlain struck a hat-trick for England U21 against Iceland this week.
Asked about Fabio Capello's recent admission that a senior call-up may soon beckon, the Arsenal winger said: "I'm just concentrating on the Under 21s at the moment. A full cap would be nice at some stage in the future, but I can't think about that now.
"We've got a really important qualifier in Norway on Monday. They are level on points with us at the top of the table, so that is going to need all our focus and attention.
"To get my first international goals and end up with a hat-trick, I'm happy with that. The most important thing is qualifying for the finals and it is going to be hard in Norway."