Jose Mourinho is believed to admire the England international and to be weighing up a move.
John Terry will turn 35 during next season, so there is naturally a search for an heir to his throne. While Gary Cahill has looked competent and Kurt Zouma promising, the Blues could still do with strengthening the heart of their defence.
The 21-year old enjoyed another excellent season at Goodison last year as he continues his development. The defender is currently with the England Under-21 squad as they compete in the European Championships but has yet to feature after suffering concussion in a training ground clash.
He is regarded as one of the most promising young defenders in European football and would aid Chelsea in meeting the home-grown quota, as per FA restrictions.
Will he leave Goodison?
Roberto Martinez will be desperate to keep hold of Stones however, and a move this summer seems unlikely.
Playing second fiddle to Cahill and Terry while competing with Zouma would not be ideal at this stage of his career and remaining at Everton surely represents the best decision for his development.