The club last week turned down a £12million bid for the left-back as former Toffees boss David Moyes returned to his old club in an attempt to cherry-pick one of their prized assets.
While that offer was rebuffed United are expected to come back with a significantly improved figure but Everton have stressed Baines is not for sale and want the 28-year-old to extend his contract beyond the existing two years he has left.
Martinez underlined the England international's importance to the club.
"I think Leighton is more than a player, he is an icon," he told the Liverpool Echo.
"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."