The champions’ second offer is a £5m improvement on their initial bid, but Everton have again refused to do business.
A senior official at Everton told Sky Sports News HQ that ‘the club have no intention of selling Stones and they have told Chelsea that twice’.
Roberto Martinez this month criticised Chelsea for going public on their interest in the England central defender, signed from Barnsley in January 2013.
The Everton manager gave no update on the situation when asked at the weekend, but team-mate Steven Naismith told Sky Sports News HQ on Wednesday he hoped Stones would stay.
The player himself said earlier this month he was “very happy at Everton”, adding: “My aim right now is to try to nail down a regular spot in this Everton team and hopefully that will take care of playing for England.
“I have to keep learning from the likes of Phil Jagielka and keep progressing at this club.”