As has been revealed, the 19-year-old centre-back is in line for a shock call-up to England's 30-man provisional squad for the tournament in Brazil after impressing Roy Hodgson in recent weeks.
And Martinez has confided that he has discussed the youngster with the England boss, who was in the stands for the Toffees' trip to Fulham last week, and is convinced he can handle any occasion.
“We spoke in the summer,” said the Spaniard. “Remember that John Stones has been in the system of the England set-up for a while now, he's been highly regarded, in the Under-21s he's had the captaincy.
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“But he is still only a young man and we need him to develop and we need to allow him to enjoy his football. But John is ready to be put in any situation, any game, any occasion. He's very much ready for whatever comes his way.”
Next up for Stones and Everton is the visit of Arsenal in a crucial clash in the battle for Champions League football, and Martinez is convinced the youngster can step up in Phil Jagielka' absence.
“I don't think there's any doubt [he can handle the occasion],” continued the Toffees boss. “His performances have been exceptional.
“In my eyes he is the complete, modern centre-half, someone that can defend in one-one-one situations, someone that is very good in the air, someone that can start the play, and he's got the composure to get on the ball. He's a phenomenal prospect.”
Another youngster flourishing at Goodison Park is Chelsea loanee Romelu Lukaku, whose agent admitted Tottenham had open talks over a potential transfer, and Martinez is keen to ensure the Belgian is not distracted by the speculation.
“There's going to be a lot of speculation and a lot of talk. Romelu has been performing extremely well, so you're going to get that speculation,” added the former Wigan manager.
“Romelu has been an incredible asset for us, the same way he's been a credit to his parent club. He's been developing. As a young man, I think he's fulfilling his potential, which I believe is huge.
“Now all we want is for him to concentrate on the next seven games and finish as strongly as can, and whatever happens in the summer it will be something good, because the season he has had it can only be positive.
“I think the next seven games are going to be very important to see where the next chapter is for Romelu, but it's not about whether we get into the Champions League or not, it's more about the focus of the football club.”