The defender is being courted by the Premier League champions this summer.
Chelsea and Jose Mourinho have made no secret of their interest in the young England international, and Everton have already rejected moves for the player.
But one former Merseyside defender is adamant that Stones should stay where he is.
Jamie Carragher, a former Liverpool player and Anfield legend, wrote in his Daily Mail column yesterday about the potential move.
He says Stones must stay with Everton for the next two years at least: “It has been a summer to make John Stones’ head spin.
“He should ignore the noise, though, and stay right where is. The best place for him for the next two years is Goodison Park, working with Martinez.
“Why? For starters, it is the style of play Martinez implements. Stones is a great reader of the game, composed in possession and starts attacks from the back. Martinez will encourage him to develop those skills.
“There will be mistakes along the way, playing in that fashion, but Martinez would be more tolerant of them. I wouldn’t expect that to be the case with Jose Mourinho.
“Will Stones play every week at Chelsea? No. The problem with playing as a centre back is that defenders don’t tend to get rotated — rightly so — and that could mean long periods out of the team.
“That time will come but hasn’t arrived yet and there are still elements to his game that he needs to improve.
"Any slip-ups along the way will be dealt with more leniently at Everton, rather than in the glare of supporters and the media talking about a £30million player. That is why the best place for his development is Goodison Park.”
Stones is set to be an undoubted starter at Everton this season alongside England international team-mate Phil Jagielka. With Sylvain Distin moving on to Bournemouth, he has no real competition.
With that in mind, he is set to get plenty of first-team football at Everton this term. At Chelsea he would be competing with Terry, Gary Cahill and Kurt Zouma for a first-team berth – meaning he would spend most of his time watching from the sidelines.
A Liverpool legend he may be, but Carragher is certainly speaking sense. The Everton lad would do well to heed his advice.