Barry has only missed two Premier League matches for the Toffees since he signed on loan from Manchester City in September and his maturity and experience has been a major asset to Martinez.
City already have plenty of midfield options so they are highly unlikely to renew Barry's contract when it expires in the summer.
Martinez previously stated he would only decide whether to offer Barry a permanent contract at the end of the season, but he now appears to have made up his mind regarding the 32-year-old England international's future.
"Gareth knows that he can stay at Everton as long as he wants to," said the Spaniard.
"He is a unique footballer. When he came here, I wanted him to be very important for Everton, to enjoy his football.
"He is enjoying his football. He is an incredible leader. All I want is for him to keep doing this until the end of the season and then, in my eyes, he should be helping England in the World Cup."
Get him in and get him signed, I think he will stay and we will be all the better for it. With Mata joining Utd I dont see why signing Lukaku is beyond the reals of possibilty- boggo