According to the Mirror, the Toffees have refused to countenance a sale at the price offered by the reigning Premier League champions.
The tabloid reports that Roberto Martinez’s side are holding out for a £34 million bid for Stones, which would represent a British record fee for a defender.
Chelsea’s latest disappointment comes on the back of a recent offer of £20 million, which was also turned down outright by the Merseysiders.
The Pensioners appear keen to secure their man, however, and may yet return with an improved bid in order to snare the England international.
It remains to be seen whether Stones himself will do more to provoke a move, with the defender understood to be keen on a switch to the London side.
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The defender appears to have been earmarked by Jose Mourinho as an ideal long-term successor for club captain John Terry.
However, Chelsea may yet face competition from Manchester United; the Red Devils are also understood to be keen on the former Barnsley man, and with the prospect of signing Sergio Ramos appearing to diminish, they may yet look to move for 21-year-old Stones.