Liverpool great Jamie Carragher reckons the England international should remain at Goodison Park.
"Every player should want to play at the highest level and win trophies, play in the Champions League and play for his country," Carragher told talkSPORT.
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Mourinho is keen on Stones and Juventus midfielder Paul Pogba
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"That's the aim of every player. It's just [a question of] what is the right time for the player to go and I think the right thing for John Stones would be to play for another couple of years at Everton.
"He's playing really well, but you have ups and downs as a young player, especially as a defender, where you can make a couple of mistakes, give away a penalty, and your confidence goes. That's part of being a defender and learning your trade.
"I think it would be better for him to know he's almost guaranteed to play week in, week out for Everton, go through those times with Everton, and then when he eventually gets his move to a top English club, as he will do, he'll be going there a bit more experienced, a better player, and a bit more mature in his game."