Manchester United have already failed with one bid for the England left-back this summer as David Moyes targets a reunion with his former player.
And Moyes' Goodison Park successor has made it clear he does not want to lose the 28-year-old.
"I think Leighton is more than a player, he is an icon," Martinez told the Everton website.
"He represents a lot about our football club and I am really, really excited about Leighton. This is a big season for him and for us as a club.
"When you are the left-back of this football club, and the level that he has been reaching over the last few years consistently, it shows me that he is the best left-back in the country. I can't wait to start working with him."