The incoming manager has made it a priority to keep last season's player of the year, who was linked with a move to Manchester United even before David Moyes' appointment as Sir Alex Ferguson's successor.
Baines' contract has two years to run, but Martinez is keen to make a statement of intent by rewarding the England left-back's consistency.
He told the club website: "It is very important and it's a case of rewarding players who have been phenomenal for the football club. I think Leighton is in that category.
"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 to the next chapter of his career with Everton.
"That's important for the club as a whole, not just the dressing room."
Everton chairman Bill Kenwright is also desperate to hold on to Baines, and he said recently: "I have told David Moyes not to come back for him."