The 33-year-old was omitted from Roy Hodgson's 23-man World Cup squad despite enjoying a successful loan spell at Goodison Park last term, helping the Toffees to a Europa League berth.
However, Barry, who has not featured for the Three Lions since May 2012, hopes that he can reinvigorate his England ambitions after completing a Bosman move to Everton earlier this week.
"You watch England's games and still want to be playing, singing the national anthem," he told the club's official website.
"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."
Barry has earned 53 England caps throughout a 12-year international career.