Barry has been a regular in the Spaniard's Everton sides and despite being 34 years old, Martinez feels the midfielder has more to offer the game.
Martinez has backed the former England man to copy the example of Ryan Giggs and continue to play into his 40s.
Martinez said: "Those players [like Giggs] are a very special breed, not just because of the natural element but also the lifestyle and the way they live the game. Football is a passion and Gareth is that type.
"Everything he does, he does for a purpose, the way he trains is as a leader, he is an inspiration to the other players and he could go on and on and on until the body has enough.
"He is a very, very fit footballer, but he plays with his brain and his technical ability allows the others to be effective around him.
"Clearly, he can play for a few more seasons at the level he is playing. Gareth is enjoying his football and is a very important football man and the way he lives his life and the way he trains is the secret of having such a long career."