The midfielder has starred for Roberto Martinez's side this season, making 18 appearances and scoring three goals in all competitions.
Barry's form – aided by the terrific efforts of Ross Barkley, Seamus Coleman and Romelu Lukaku – has helped Everton to sixth in the Premier League, just two points off the top four.
Everton are realistic contenders for a UEFA Champions League berth, and Barry is hopeful of making his switch permanent at the close of the season.
"When I see them (Everton fans) they say: 'You'd better be signing next season!', Every time!" Barry told The Telegraph.
"My answer is the same every time: 'Hopefully! Hopefully!', That's a genuine answer.
"From day one, the manager said: 'I'm not going to put any pressure on you throughout the season, we'll have the conversation in the summer, see how the club feel about you, see how you feel about the club and take it from there.'
"I'm more than halfway through the season now and it couldn't have gone any better.
"It's going to be a nice conversation to be having come the end of the season."
Barry also remains hopeful of regaining his England place ahead of this year's FIFA World Cup in Brazil.
The 32-year-old, who has won 53 caps for his country, says that regular praise of his performances this season has renewed his belief of being on the plane to South America.
"The more people have mentioned it (an England return), the more I start thinking about it," he added.
"I'm not going to turn down a call for England if it comes. I've maximum belief that if called upon, I can do a job for England.
"I have that real belief inside me. I'd like to think I'm not too far away from being one of the better players in the set-up at the minute."
