Blues boss Roberto Martinez believes Barry can play into his 40s.
Barry recently became the 10th player to reach 500 Premier League appearances and plans to carry on as long as possible.
"I've always said that I want to play as long as possible and as long as my body and legs allow me to do so," he told evertontv.
"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 took 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."
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