Blues chiefs are keen to extend Hazard's current terms, which are due to expire in 2020, while goalkeeper Courtois is available on a free transfer in 18 months' time.
Belgium international Hazard has rejected suggestions that he is delaying talks over a new deal, but says he first wants compatriot Courtois to commit.
Asked if he will sign a new deal, the 27-year-old told The Mirror: "Yes. I think Thibaut first. Then I will sign."
Hazard has scored nine goals and set up four more in 27 appearances for Chelsea this term.