The England international has said that a decision will be made in the summer, but has confirmed that Champions League football will not be a factor.
"I'm desperate for this club to qualify for the Champions League," Barry told Sky Sports News. "But in terms of my future and Everton being in the Champions League or Europa League, I don't think it will have any effect on my decision.
"I definitely want to play as long as possible, as long as I'm playing to a standard I'm happy with. Roberto and I spoke at the beginning of the season and said we would look at it at the end. We said we would see how it goes. See where we are.
"I will make my decision on my future then. If the club offer me a contract and show me they want me, then it is a possibility."
Barry has made 34 appearances in all competitions for the Toffees this season, scoring three goals.