The American keeper's current deal ends in the summer and whether he is likely to remain at Goodison Park in the long run remains unclear.
Martinez has paid tribute to his contribution but will not say what is likely to happen next. He said: "Tim is one of those foreign footballers who has brought so much to the Premier League.
"It is not normal to get a foreign player to get so attached to a football club, especially in the modern game.
"To have 10 seasons like Tim is having now is an incredible contribution and all I'm focused on is making sure he gets back to his best level and finishes the season strong.
"Whatever happens in the future, I don't think it is the right moment to speak about it now."