The 19-year-old, who arrived at Goodison Park from Barnsley in January, has made just four appearances for the Toffees during the current campaign.
Despite his lack of first-team action, Martinez is confident that the right-back can continue to learn if he stays at the club.
"I think he can develop here fighting for his place," the Spaniard told the Liverpool Echo. "He's earned that and I don't think he needs to go out on loan and play.
"He's got an incredible future which we're all excited about and we're looking forward to him fighting to see how quickly he can get in the team."
Everton continue their Premier League campaign on Saturday when they make the trip to strugglers Crystal Palace.