The 19-year-old moved to Goodison Park at the beginning of the campaign on a temporary season-long deal from La Liga champions Barcelona and scored the equaliser in Everton's 1-1 draw at Arsenal on Sunday.
"We have an agreement to extend the loan for an extra year if Barcelona don't need Deulofeu," manager Martinez told reporters. "He has incredible pace and I've never seen a player so quick with the ball.
"You've got certain players with raw talent who can create from nothing with a special touch and he is one of them.
"I always thought he'd take until February to learn how to deal with the league but he's surprised me. He's very arrogant in the right way and today's finish is exactly what he deserves."
Deulofeu, who has scored three times in all competitions, has impressed since joining Everton.