The England left-back has been a transfer target for Manchester United in recent months but Martinez is confident he will want to sign a new contract with the Toffees.
"He is in the best moment of his career and has got a real maturity which allows him to think on the pitch and make good decisions.
"He's not just a player, but a real icon of our football club, so clearly we want him to stay as long as we can.
"There is nothing to announce at the moment, but the way he's playing, he's looking to try to progress and develop.
"He is a player that you can imagine everyone at the football club would love to see him enjoying his football here for a longer period."
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