Barry has not featured at international level for 17 months, with the last of his 53 caps coming in Hodgson's first game in charge against Norway last May.
Martinez believes that Barry still has plenty to offer Hodgson, particularly in a Three Lions squad which is increasingly full of more youthful options.
He told The Mirror: "I see Gareth as a very, very valuable option for England.
"What he brings onto the pitch is very difficult to find. There are few players who can bring that experience, that know-how, that tactical awareness, and he will always be a man who can offer a lot to the national team.
"Whether that's needed in the World Cup or not depends on circumstances, but often it is. And Gareth has such high standards in everything he does, we will see a very important player for Everton."
The 32-year-old has settled quickly under Martinez at Goodison Park, after making a summer loan switch from Manchester City in search of first-team football.