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United manager David Moyes, Martinez's predecessor at Goodison Park, had an initial bid for Baines rebuffed last week when Everton rejected an offer of 12 million ($18.3 million, 14.1 million euros) for his services.
The English champions are expected to return with an improved bid for the 28-year-old set-piece specialist, but Martinez says Baines is an important part of Everton's future.
"I think Leighton is more than a player; he is an icon," Martinez told local newspaper 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."
Martinez is reportedly close to completing moves for striker Arouna Kone and centre-back Antolin Alcaraz, with whom he worked at previous club Wigan Athletic, and he said that both players would be valuable additions to the Everton squad.
"They are players that I know really, really well.
"I worked with them really closely and they are players that are used to the Premier League and the British game," Martinez told Everton's in-house television channel, evertontv.
"You will always get those sorts of situations, but at the moment we are still looking to try to bring the right characters to the football club.
"We need to remember that we have a very strong team at the club, but in the same way, we don't want to close the (transfer) window without feeling stronger than we were when the window opened.
"I think we need to bring in three or four new faces -- one per unit (goalkeeper, defence, midfield and up front) and make sure we get an extra option or dimension into the squad."
Martinez met Everton's players for the first time on Wednesday as they returned for the start of pre-season training.
"The most important aspect is to try to keep the squad together and get every player ready," he said.
"I have been able to speak with the majority of them and as a manager you can't wait to get to know the players and how they think and where they are physically.
"It is important we have a successful pre-season because it is a time when you can set certain aspects, which can help us at the start of the season."
