The defender has been the subject of a bid but Keown doesn't believe he should leave Goodison Park.
The young defender has been the subject of a £20 million bid from Jose Mourinho’s side earlier this week, although his current club swiftly rejected the offer.
The Premier League champions are expected to come back with an improved bid for the defender at some point in the future and are keen to secure the player despite Everton not being keen on a sale.
And Keown has urged him to stick with the Toffees and continue his development in their side.
"Chelsea are moving now probably because they can see he’s going to be the player they want but I’d rather see him play at Everton," he told talkSport.
"I think he’s going to be an outstanding talent but I don’t think he’s the finished article by any means. There are things for him to work on and he would be better doing that at Everton. It would be best if he was left for another season."
First-team football guaranteed at Everton
Stones is easily one of the brightest talents of his age at this moment in time, having enjoyed an impressive rise in the Everton first team.
It is arguable that a place in Roberto Martinez’s side has aided his rapid development, with the exposure to Premier League football and working alongside Phil Jagielka clearly a big bonus to him.
First-team football is something that would be hard to come by at Chelsea, though, with John Terry and Gary Cahill first choice, and Kurt Zouma impressing when given the chance last season.
That competition may see his development stunted, meaning a stay at Goodison Park could be better for his career at this moment in time. But whether bigger money tempts both him and Everton remains to be seen.