The 28-year-old is said to be a main target for Manchester United, who are believed to have failed in their opening bid for the Everton star.
"I think Leighton is more than a player, he is an icon," the Liverpool Echo quotes Martinez as saying. "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."
Reports have claimed that United will return to Goodison Park with a fresh offer for Baines.