Stamford Bridge side keen to spend before the transfer window slams shut.
The Blues have already failed with offers of £20m, £26m and £30m for the 21-year-old England international and may be ready to stump up a massive offer of £40m, which is believed to be one that Everton would accept.
Jose Mourinho has seen his side start their Premier League title defence poorly with Chelsea opening the campaign with a 2-2 home draw with Swansea City before losing 3-0 away at Man City on Sunday.
During the Etihad Stadium encounter Mourinho surprisingly elected to sub captain John Terry at half-time and this has only heightened speculation that Chelsea are ready to spend a huge sum on a new defensive addition.
What might prove the biggest selling point with regards to Chelsea’s interest in John Stones is the fact that the former Barnsley man can operate as a very effective right-back, as well as in his primary role as a central defende, with Mourinho having seen Branislav Ivanovic horribly exposed by Swansea City’s Jefferson Montero and Man City new boy Raheem Sterling already this season.