The 19-year-old is yet to start a Premier League fixture, but he is pushing for a first-team place at Goodison Park.
The England U21 international joined Everton from Barnsley in January.
Martinez told the Liverpool Echo: "I think he can develop here fighting for his place.
"He's earned that and I don't think he needs to go out on loan and play. Here he is learning on a daily basis from Jags (Phil Jagielka) and (Sylvain) Distin, and that's exactly what he needs.
"He's not the same player from pre-season, he's already gone to a different level.
"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.
"Every player is an individual and needs different things.
"John has had first-team experience. He played enough with Barnsley in the Championship to know what to expect."