The England international was the subject of heavy interest from Manchester United in the transfer window, with David Moyes looking to his former club for deals after swapping Goodison Park for Old Trafford.
A double bid, widely reported to be for Baines and Marouane Fellaini, was rejected and labelled "derisory" by the Merseysiders, but the Belgian did eventually make the switch to United - for £27.5million on deadline day.
However, with Baines remaining, he is set to be rewarded for his loyalty with an extended contract.
Martinez explained: "What’s important is to show Leighton how much we want him and how much we appreciate him. Sometimes you need to do it with actions, not just words. That’s going to be the case.
"It’s about looking for that football happiness and I guarantee to everyone that Leighton will enjoy his football and his role at the club.
"We need to make sure he understands that he is a vital part of the football club and the team and sometimes that needs to be rewarded from a contractual point of view, and we will do that."
Everton have begun life under Martinez with three draws from as many Premier League fixtures and the Spaniard is delighted to have hung on to his star left-back, who scored five goals and racked up seven assists in an ever-present top-flight campaign last season.
"Leighton is a vital player for us," he continued.
"We couldn’t replace a player like him. There was a lot of talk and speculation, but no one met his valuation so in that case he remains with us.
"Now we need to make sure that he understands how important he is for the football club and he needs to get that reward from our point of view.
"We need to make sure we are ready for the competition ahead with one of the most influential players in the history of Everton.
"We are in a position where unless a club meets a player’s valuation, there will never be a decision made. That was the case with Leighton."
