The Three Lions defender has been the subject of speculation in recent weeks, following a big-money bid from Premier League rivals Chelsea.
But the 21-year-old hasn't let that affect his performances and the former Barnsley man was part of the defence which helped Everton to secure a clean sheet and a point against Tottenham Hotspur on Saturday.
Stones was impressive in Everton's draw with Spurs at the weekend
"He's such a professional," said Everton boss Martinez.
"With John, it's very easy because he's a pristine professional. Obviously he's been put under massive, massive pressure.
"[On Saturday] you saw a 21-year-old deal with that pressure and he played in that manner.
"For me, it shows he has potential to be England captain.
"The way he has always been performing - he's always been a top professional, never letting the team down or the football club down. He is a true Evertonian."
Stones was named in Roy Hodgson’s latest England squad on Sunday evening as the Three Lions prepare to face San Marino and Switzerland in their next two Euro Qualifying games.
