The 33-year-old midfielder signed a three-year contract at Goodison Park earlier this week, after impressing during his season-long loan from Manchester City last term.
Barry, on his last appearance for England, against Norway in May 2012
After picking up his last cap for the Three Lions in the game with Norway in May 2012, Barry admits that his chances of a recall under Roy Hodgson are limited.
But the former Brighton & Hove Albion and Aston Villa star, who has 53 caps for England, still has an eye on the international scene and would be willing to make a return.
"I’d probably say my chance has gone now," he said. "If it was going to happen, it probably would have come after a good season last year.
"But I’ve not retired in terms of international football and in football, you never know."
Barry is now back in pre-season training with Roberto Martinez’s squad ahead of the new campaign.
He made 32 appearances in the Premier League last time around and is hoping for a similar return this time around as the Toffees chase a top four spot.
"My focus, like it was at the beginning of last season, is to work hard with Everton," he added.
"If I can keep playing well and get in the England squad, that will be my aim again this season."
