The 32-year-old joined the Toffees on transfer deadline day after becoming surplus to requirements at Manchester City under new boss Manuel Pellegrini.
Barry has not played for England in more than a year, but Martinez believes he could again play for his country.
"He has an ambition to play for England again and that's very important, not just for the future, but for the games now because at 32 I consider him at his peak," Martinez told the Daily Mirror.
"I see him getting back in the England team because there are not many like him.
"His role is very specific and usually filled by a foreign player. It's not the type the English game usually produces well, so if he reaches his best level with us, he will be a massive asset again for England.
"I've always admired Gareth because he is a unique midfielder in the English game. You don't get many midfielders like that in the English game with his tactical awareness to his play.
"He has won the league and FA Cup. Normally in England you get the box-to-box midfielder, but Gareth brings a more continental approach.
"It will be different for Gareth here because our aims are different and the football club is different.
"Each player has his role, but I just want him to enjoy his football and bring his highest standards to the side. Just working with him has been fascinating to see how he works and his know-how."