The left-back played every minute of the Toffees' Premier League campaign last season, prompting speculation that former boss David Moyes is keen to bring him to Manchester United.
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"It is very important and it’s [a case of] rewarding players who have been phenomenal for the football club, and I think Leighton is in that category," Martinez told the club's official website.
"The chairman is very keen to express that and obviously I’m desperately looking forward to meeting the players.
"For Leighton, as the top performer he has been in the last few years, it is important that we reward his work and make sure that he can look forward to kicking-on and go into the next chapter of his career with Everton.
"That’s important for the club as a whole, not just the dressing room."
Baines was included in the Professional Footballers' Association's Team of the Year before being named both Everton's Player of the Year and Players' Player of the Year last season.