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Barry's maturity and experience came in handy on Saturday as Everton came away from League One Stevenage with a comfortable 4-0 win in the fourth round of the FA Cup.
Barry has only missed two Barclays Premier League matches for the Toffees since he signed on loan from Manchester City in September.
City's squad is awash with midfielders so they are highly unlikely to renew Barry's contract when it expires at the end of the season.
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's future.
"Gareth knows that he can stay at Everton as long as he wants to," the Everton manager said.
"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."
Barry was one of the first players to rush to help Bryan Oviedo after he broke his left leg in two places at the Lamex Stadium following a clash with Stevenage midfielder Simon Heslop.
Oviedo looked set to play a key role in Everton's push for Champions League football, but instead he is likely to miss the rest of the season and the World Cup, much to the dismay of striker Steven Naismith, who scored twice for Everton on Saturday.
"We came to win and we went ahead but then that horrible thing happened to Bryan and he is the main concern for us," the Scot told Everton TV.
"This was probably the first time in his Everton career where he has had a run of games and he has shown his potential.
"Everyone has been able to see what he has got and everyone in the team will be looking out for him now."