Blues boss Jose Mourinho is believed to be extremely keen on completing a deal for Stones, however, Everton are desperate to keep hold of one of its most prized assets.
The Toffees reportedly value Stones at a massive £34m, and Chelsea are yet to have matched the Merseyside club’s valuation of the England international.
According to the Daily Star however, the Premier League champions have been handed a glimmer of hope with Everton reportedly keen on making a move for Williams should the club lose Stones.
Chelsea’s defence was torn to shreds by the Manchester City attack on Sunday, and Mourinho will be keen to bolster his squad before the end of the transfer window.
Everton have also been linked with a move for £7m-rated Napoli centre-back Kalidou Koulibaly.
5 things learned from Arsenal’s 2-1 win at Crystal Palace: Cech, Coquelin, Alexis & Giroud in focus
Arsenal player ratings v Crystal Palace: Giroud & 9/10 MOTM shine in deserved Gunners win
Video: Crystal Palace 1-2 Arsenal – Giroud stunner and strange own goal get Gunners back on track