Stones lost his place in the City side during the second half of the 2017-18 campaign, initially going down with an injury and then being unable to force his way back in ahead of the likes of Nicolas Otamendi, Vincent Kompany and Aymeric Laporte.
The 24-year-old still did enough to earn a place in the England squad for this summer's World Cup, though, where he could come up against Martinez's Belgium side in the group stages.
Martinez previously managed Stones at Everton, handing him his Toffees debut, and the Spaniard is confident that the player will go on to enjoy a successful career.
"I was scouting John for Wigan and we missed him on deadline day, and then he signed for Everton in January 2013," Martinez is quoted as saying by The Mirror.
"He hadn't made his debut when I joined Everton that summer, but, from day one, I knew John had to be a centre-half and he had the composure on the ball to play there.
"It was a really interesting journey to see him grow and taking responsibility and get to the level he has got to. He has a big future."
Belgium and England will face off in their final group game in Kaliningrad on June 28.