Barkley has only made a handful of appearances for the Toffees since turning professional in 2010 and has had loan spells with Sheffield Wednesday and Leeds United.
However, Martinez has been impressed by the 19-year-old during their pre-season campaign and he continued his good form by setting up Everton's opening goal in Saturday's 3-1 win at Blackburn.
"He is something special," Martinez told the Liverpool Echo. "In football when you describe a player, there are not many better descriptions than to say he's an incredible football diamond.
"He's still a young man, and he needs to learn the players around him, but I'm excited to have that process with him. He has got an incredible talent.
"You look at young players like Gerard Deulofeu and Ross Barkley; they are at that level.
"I am really pleased with his attitude, the way he listens and wants to learn. And when he is in full flow, he can be something special."
While confident Barkley can make a positive impact in the Premier League, Martinez stressed that Everton need to find the right partnerships around the midfielder in order to help him realise his true potential.
"Ross is such a talented boy, and has an incredible appreciation of space, that he can play in many positions," said Martinez.
"Of course you want him as high up the pitch as you can because he can be lethal with his finishing ability.
"But it is about finding the right partnerships around him. At the moment he is a young man who is still learning when to use his talent and when he needs to do things for the team.
"The early signs have been really good and encouraging."