The midfielder left Manchester City for Everton in a one-year loan deal in the summer and has helped his new club win 12 points from their opening seven league games.
The 32-year-old's form has not been enough to attract Roy Hodgson's attention, though, and he remains without an England cap since June 2012.
But Barry still has ambitions to add to his 53 international appearances, and he told the Everton website: "It's something that I definitely wouldn't be turning down at the moment.
"I joined Everton to play regular football and that's still my main target, to get my form going. If an England call comes with that, then fantastic.
"I've always said that I want to play as long as possible and as long as my body and legs allows me to do so.
"At the moment I'm feeling good and really fit, and I'm hopeful I can play for a number of years.
"But I've always taken one season at a time, and this season I'm looking at keeping a good run of form going and helping Everton climb the table to see where it gets us."