The young attacking midfielder, who scored the equalising goal against Arsenal on Sunday, has surprised the Toffees boss with his quick adaptation to English football
The Spanish attacking midfielder netted a late equaliser against Arsenal on Sunday, his second goal since arriving at Goodison Park in the summer, and the Toffees boss hailed the speed of his adaptation to English football.
"We have an agreement to extend the loan for an extra year if Barcelona don't need Deulofeu," 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 [Sunday]'s finish is exactly what he deserves."
Ross Barkley was another standout performer as Everton held the Premier League leaders at the Emirates, prompting renewed talk about the youngster's potential inclusion in England's World Cup squad, though Martinez intends to carefully manage the midfielder's development.
"The England manager [Roy Hodgson] has to decide what role, if any, he wants for Ross [at the World Cup]," he observed.
"What we need to do is make sure we give Ross another 50 starts to see his evolution. Any player needs to develop an understanding.
"In this country, we need to be more protective over our youngsters because, in Ross, we have someone who, if we look after him properly, can give us something unique."