The Blues youngster put in another good performance against Manchester City on Wednesday.
The young defender was Moyes’ last ever signing as Everton manager for £3m from Barnsley in 2013 before he left to manager Manchester United.
He has since gone on to become one of the most highly regarded young defenders in European football, with a series of impressive performances in Roberto Martinez’s first team.
He is also now a regular in Roy Hodgson’s England team, and Moyes has backed him to have a bright future in the game.
"This boy's coming on like nobody. He's coming on with great quality and great ability on the ball,” he told Sky Sports.
“He's improved his overall defending, he's got a natural ability to take the ball which is not something that's coached. He's reading the game much better.”
“Obviously he's going to go on and play for England for a long time. John will go on to big things, I've no doubt about that."
If Stones continues to impress as he has, and has a good Euro 2016 should he be selected by England, interest is sure to rise in him from Europe’s big clubs.
There was already interest from Chelsea in the summer, and another impressive season this year will not have dampened the widespread regard for him.
The summer transfer window could be a defining one for the Blues then, with clubs likely to test how much money they are willing to reject for their young starlet.