The England international came close to joining the Blues last year after a stunning breakthrough campaign at Goodison Park.
Chelsea openly chased him for much of the summer, yet despite a £37m offer as the transfer window ticked towards the deadline, the Toffees held firm to retain their man.
The club have since been very vocal on their desire to keep the 21-year-old, but reports claim that the defending Premier League champions remain keen and are willing to offer £40m.
However, they will face a battle with Barcelona, who have been monitoring the classy, ball-playing defender.
The Catalans are understood to see him as the sort of player who could function in their side, where technical prowess is appreciated in defensive players.
Chelsea may be more desperate than their Spanish counterparts, with the Stamford Bridge side having already shipped 29 goals in 20 league matches this term.