Barry has impressed during his season at Goodison Park and his contract at parent club Manchester City expires at the end of the campaign.
Everton boss Roberto Martinez has previously confirmed that he wants to keep the 33-year-old and Barry is keen to ensure he makes the right decision regarding his future.
"The manager made it clear we'll discuss things in the summer and to concentrate on football, that's what I need to do," Barry is quoted in The Sun.
"Let's focus on the end of the season, hope it is successful and take it from there.
"I'm 33 so it will probably be my last contract. I want to make sure it is the right one."
Martinez has also sparkled at Everton this season in his first year in charge and he has the club in contention to finish in the top four.
Everton currently trail Arsenal by four points, but have a game in hand and face Arsene Wenger's side at home on Sunday.
Barry added: "A few weeks ago, Arsenal were looking at the title, now they are looking behind them. That's how quickly things can change."