Roy Hodgson's men are not seen to be among the main contenders in Ukraine and Poland, but Los Angeles Galaxy man Beckham refuses to be pessimistic.
"I think we're going to go to the European Championship and surprise a lot of people," the 37-year-old told the Mail on Sunday.
"Expectations are not as high as they have been in previous competitions but we're talking about England here. No one can doubt the talent or the passion we have."
England have been hit by injuries, with midfielders Frank Lampard and Gareth Barry ruled out.
And further doubts were raised about defenders John Terry and Gary Cahill after they picked up knocks in Saturday's win over Belgium.
Beckham is not expecting a recall, though.
He said "I don't expect a call-up, but there's a reason why I haven't retired from international football, that I've not said 'That's it', even at 37 years old.
"I always want to represent my country and I always want to be part of any England team.
"I doubt it will actually happen again. But there's always a chance. I'll never say never."