The 21-year-old has long been a target for Newcastle but the Blues are now keen to sign the winger-turned-striker from the cash-strapped Toffees.
Everton could be ready to sell Gordon who they have valued at £45m with Frank Lampard keen to raise funds to reinvest in his squad that currently lacks a top striker.
The move adds Gordon to a long list of Chelsea targets with Pierre-Emerick Aubameyang another key target in attack.
There's also fellow Barcelona star Frenkie de Jong who has long been Manchester United's primary midfield target.
Thomas Tuchel also wants to add a defender and has seen two bids rising to £70m turned down by Leicester for Wesley Fofana.
Tuchel wants to add at least one more player but preferably more with several members of his squad angling for moves.
Among those wanting to leave are attackers Hakim Ziyech and Callum Hudson-Odoi.