Baines has 18 months left on his current deal at Goodison Park and he was targeted by Manchester United during the summer transfer window.
It is understood the England international could sign a new deal this week and Martinez is keen for the 29-year-old to stay at Everton in the long term.
"You know how important he is for us," Martinez told Sky Sports following Everton's 1-1 draw at West Brom.
"He is in the best moment of his career and has got a real maturity which allows him to think on the pitch and make good decisions.
"He's not just a player, but a real icon of our football club, so clearly we want him to stay as long as we can.
"There is nothing to announce at the moment, but the way he's playing, he's looking to try to progress and develop.
"He is a player that you can imagine everyone at the football club would love to see him enjoying his football here for a longer period."
The Everton manager also confirmed he is looking to strengthen his squad to compensate for long-term injuries to forward Arouna Kone and midfielder Darron Gibson.
Martinez has also sold Nikica Jelavic to Hull City and has been linked with a loan move for Monaco's new signing Lacina Traore.
He added: "Obviously we've got two players out with long-term injuries - Arouna Kone and Darron Gibson - and they are the two positions we want to be as strong as we can be between now and the end of the season.
"We want to get everyone fully fit to make sure we finish the season as strong as we can."