The clamour for Arsenal winger Oxlade-Chamberlain to be a wildcard pick for this summer's finals has grown since the start of the year, with the 18-year-old having earned rave reviews for his performances in the Barclays Premier League and Champions League.
Oxlade-Chamberlain told Arsenal Player: "It would be very nice but I don't get too far ahead of myself or get carried away."
Oxlade-Chamberlain was controversially omitted from caretaker England manager Stuart Pearce's first squad for February's friendly against Holland, denying him his maiden senior cap.
But Pearce insisted he would consider taking the Under-21 star to Poland and Ukraine were he to remain in charge this summer.
England are currently without a permanent manager or captain following Fabio Capello's shock resignation almost two months ago, with neither vacancy set to be filled until the end of the season.
It is a far-from-ideal state of affairs leading into a major tournament but Oxlade-Chamberlain believes they have the players to triumph this summer.
"There are a lot of good teams like Spain and Holland, but you have to say England have what it takes to get to the final and even win it," he said.
"We have a lot of really good players in this country and a lot of experienced players."
Oxlade-Chamberlain is one of several Arsenal youngsters who have put their hands up for EURO 2012, with Jack Wilshere and Theo Walcott also in the frame.
He said: "The fact that they are pushing on already and are in the England squad, while playing week in week out in the Premier League, can only be good.
"There are a lot of English players coming through, such as the likes of Danny Welbeck and Kyle Walker, while at Arsenal we have the likes of Jack Wilshere and Theo.
"As long as everyone keeps progressing as they are at the moment, it will be good for England's future.
"We have a lot of English talent here at Arsenal and we will all be working hard to get into the national team.
"The longer you play with people, the better you get to know them.
"You bond, and being around the same players means that you bounce off each other. It will be good for the future.
"For their age, they are all really mature and fearless.
"You forget how young Jack is - he is such a confident lad - but at the same time they are all humble as well.
"When it comes to football, they are really focused and just get on with the job.
"They are technically very good and have the right mindsets to become world-class players."
Oxlade-Chamberlain knows he must continue performing for Arsenal if he is to stand any chance of booking a place on the plane to Poland and Ukraine.
The Gunners are currently in a four-way battle to secure Champions League football next season, with arch-rivals Tottenham level on points with them in the Barclays Premier League and Chelsea and Newcastle a further five behind.
Oxlade-Chamberlain added: "My main focus is to see the end of the season out with Arsenal and help us do as well as we can.
"We have a long way to go to get a Champions League spot and hopefully top three as well.
"It would be very nice, but one step at a time is the way to go."
Meanwhile, rookie goalkeeper Damian Martinez wants to follow in Wojciech Szczesny's footsteps by starring on loan at another club before returning to challenge the Pole for the number one spot.
Szczesny made his name during a spell at Brentford that ultimately helped him break into the Gunners' first team.
Martinez, 19, said: "Wojciech said he wasn't ready for the first team yet so he went out on loan and learned so much there.
"Next season, a loan spell could be an option for me."