Everton supporters may grimace at such a suggestion given City took the £47.5million defender from Goodison Park just as Koeman was settling in as Toffees manager this summer.
But the 22-year-old has slotted in well at the Etihad Stadium and City boss Guardiola can see qualities in him that he previously saw when playing alongside Koeman at Barcelona.
“They’re quite similar in the sense that they both like to play the ball,” said Guardiola, whose side host Koeman’s Everton on Saturday.
“Normally, a central defender is a big guy who plays with the head and marks man to man and is strong in the air. We need that, of course, but now it’s the added plus of the quality of his play. John has similarities to Ronald, especially in terms of mentality.
“John is a guy who wants to play under pressure. Normally, the players who like to play the ball handle the pressure better than the other ones.
“Ronald was by far one of the best central defenders I’ve ever met. I cannot compare now, not yet, but maybe in the future.
“The long balls are always… wow. Ronald was the best ever at that. But John is young enough that he can improve.
“I am so glad that he played for the national team and did well. In the last European Cup (Euro 2016) he didn’t play one minute. Now he’s playing all the games and he’s becoming an important player for the national team. I am so happy about that.”
Stones’ final season at Everton was an inconsistent one but such has been his progression under Guardiola that he already looks to be a key component of the new City era.
Asked how Stones had managed to settle so quickly, Guardiola said: “Because he’s good. There’s no secrets, in football the good players adapt quickly and John is good and adapts quick.”