The Toffees are desperate to hold on to their 21-year-old defender who has already played for the England senior team.
Stones made his England debut just two days after celebrating his 20th birthday, with many predicting a long and successful future for the former Barnsley player.
And 37-year-old Distin, who recently joined Bournemouth on a free transfer, praised Stones for his attitude on and off the pitch.
The French defender told Sky Sports News HQ: “He’s young, English, full of qualities and a good guy as well.
“I’ve often said it’s not enough to have quality on the pitch. Off the pitch you need to be grounded and a good person – and he is.
“So it’s not surprising a big club has come in for him. It is a compliment and if he carries on the way he has started and keeps working, he’ll end up at a big club – that’s for sure.”
When asked whether he believes Stones can reach the pinnacle of the England game, Distin added: “He hasn’t played a full season yet. So he needs to become a little more experienced, understand the Premier League and know a bit more about himself, and then you can speak of it.”