The 18-year-old midfielder has already made one appearance for the Toffees first team, coming on as a substitute in an academic Europa League tie against Kuban Krasnodar in December 2014.
He has continued to shine for the club's Under-21s team, and scored with a 40-yard lob against Southampton in an academy game last week in front of the senior manager.
Martinez highlighted the skill set that the England Under-18s international boasts at such a young age and said that the teenager is bound to have a bright future at Goodison Park.
The Spaniard told the club's website: "The chip had to be perfect and - forget about his age - I don’t think there are many players in the game who could execute the action the way he did.
"You don’t get players like Kieran in the British game. He’s a player who appreciates space, enjoys playing in between lines and the technical ability he has is a natural gift. We need to allow him to develop but clearly he has got a role with the first team after that.
“He is a really humble person and strong mentally. It was a shame that he had an injury earlier in the season but he’s starting to get good rhythm and good match fitness, so I think we are going to see a lot more from him."
Martinez has allowed a number of talented youth prospects at the club the chance to step up to his first team during his two-and-a-half-year tenure on Merseyside.
Martinez has clearly earmarked Dowell as the next future star, and the youngster's progress will be worth monitoring over the next few months.