32-year-old will return to the starting line-up after missing out against parent club Man City
Barry has been an impressive performer since beginning a season-long stint at Goodison from Manchester City six weeks ago.
Having been unable to play against his parent club in the 3-1 defeat at the Etihad a fortnight ago, the 32-year-old will return to the starting line-up for the home Premier League clash against Hull City tomorrow afternoon.
And while dismissing suggestions Everton could attempt to make Barry’s move permanent in the New Year, Martinez has urged England coach Roy Hodgson to consider the claims of the midfielder – who has not figured for his country since May 2012 – for Brazil next summer.
“I see Gareth as a very, very valuable option for England,” said the Goodison manager. “Only time will tell but what he brings on to the pitch is very difficult to find.
“You don’t get many options where you have someone of that experience, that knowhow, that tactical awareness, and he will always be a man who can bring a lot to the national team.
“Whether that’s needed in the World Cup or not depends on circumstances, but Gareth has such high standards in everything he does, we will see a very important player for us with the motivation of that or not.”
Martinez added: “When you get to work with someone who’s played over 500 Premier League games you know they don’t need any extra motivation to be at their best.
“It’s not been a big surprise, because I’ve admired Gareth from a distance, but the standards he brings on a daily basis, I don’t think it makes any difference if he sees he has an opportunity or not.”
There were suggestions Everton could try to turn Barry’s loan move into a permanent deal during the forthcoming January transfer window.
But Martinez said: “No, Gareth is here until the end of the season, that cannot be affected.
“All we want is for him to be enjoying his football and effective for Everton and we'll take it from there.”
With Darron Gibson set to miss most of the season after this week suffering a serious knee ligament injury, Martinez admits he has not ruled out further central midfield reinforcements.
“We are blessed with quality in the squad,” he said. “We don't want to lose any player, but there is an opportunity now for other players in the squad, we will assess in January, but there are chances for youngsters in the club.”
Gibson ruptured his anterior cruciate ligament during the first half of the Republic of Ireland’s 3-1 World Cup qualifying win over Kazakhstan in Dublin on Tuesday.
Martinez retains hope the 25-year-old will be back playing again his campaign, and is convinced the player will emerge stronger as a result of his setback.
“With experience we know there are many cases when a player comes back stronger and mentally they are ready to take their careers on to the next level,” said the Spaniard.
“I think Darron is at the age where he will probably benefit from having that time to think, to having that frustration in his body of watching his team-mates playing.
“We need to help him get strong as a footballer and a human being while he is away, but I don't think the injury itself is as complicated these days.”
Steven Pienaar (hamstring) and Antolin Alcaraz (hernia) are both still sidelined, as is Apostolos Vellios having picked up a knock while on Greece under-21 duty this week.