Goal.com this afternoon reported that Hector's representatives are currently discussing personal terms in west London ahead of a shock deadline day move to the Premier League champions.
The 23-year-old Hector, who has made six appearances for Jamaica, has been out on a total of 11 loan spells throughout his career.
The Blues completed the signing of Papy Djilobodji earlier in the day from Nantes. The moves for the defenders put the club's hopes of signing John Stones from Everton for further in doubt.
The Toffees have rejected four approaches for the highly-rated 21-year-old this summer, the most recent being £38m.
Everton chairman Bill Kenwright had released a statement last week saying that the player would not be sold, and than he had rejected a transfer request from him.
