Baines' former manager David Moyes wants to take him to Manchester United and has already seen an offer rejected.
"I think Leighton is more than a player, he is an icon," Martínez said. "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."
"Leighton is a phenomenal performer and has become a very consistent player for Everton. A lot of people get upset when other clubs show interest in their players but I feel it is compliment. Leighton is vital for our future and what we are going to achieve at the club."