The 33-year-old has not played for his country since featuring in a friendly victory against Norway more than two years ago after being overlooked by Roy Hodgson.
England boss Hodgson has favoured blooding young players, such as Ross Barkley and Adam Lallana but Barry has not given up hope of adding to his tally of 53 caps after signing a three-year deal with Everton on Tuesday.
He said: "You watch England's games and still want to be playing, singing the national anthem.
"It's a massive buzz. As a kid, you always dream of playing for England. That's why I am still here; I've not been capped for a couple of years, but I've not retired.
"You sort of hope for that chance to come again. Any player who feels they still have a chance of playing for England and thinks maybe they should have been picked will watch the games and feel exactly the same."
The former Manchester City man made an impressive impact in a loan spell at Goodison Park last season and is determined to kick on under Roberto Martinez.
He added: "In terms of a whole campaign, last season has to be one of my best. The performances the team put out, the club record points total in the Premier League, the big wins - there were so many positives.
"But that is last season. Now we try to improve on that, and if we do improve then we are going to be going to some very good places.
"We will have to treat this season with respect. It is going to be very different with the Europa League and there are a lot more games. But I'm sure the manager will have his plans for that challenge already and I'm looking forward to it.
"The whole squad is always so keen to learn and never satisfied. From the manager, right through the coaching staff, to the players, everybody wants to improve."
