According to the Mirror's Jack Rathborn, the Belgian was asked if he would pen a new deal at Stamford Bridge and replied: "Yes. I think Thibaut first. Then I will sign."
Courtois' contract expires in 2019, while Hazard's follows a year later.
The pair were attending NBA London on Thursday, and Hazard reaffirmed his commitment to Chelsea in conversation with a fan, per ESPN UK:
Hazard is the Blues' best and most important player, so tying him down to a new deal is imperative.
While he still has over two years remaining on his contract, Chelsea do not want to find themselves in a similar situation to Arsenal with Alexis Sanchez and Mesut Ozil. The Gunners risk losing the pair on free transfers as they near the ends of their contracts.
The forward recently celebrated his 27th birthday, prompting Squawka Football to illustrate his contributions to Chelsea since he joined in 2012:
He has also been included in UEFA's Team of the Year for 2017 alongside Lionel Messi and Cristiano Ronaldo.
A player of his calibre should perhaps have posted greater numbers during his time at Stamford Bridge, which is one aspect of his game that separates him from the two superstars.
Nevertheless, he's Chelsea's most potent threat in the final third thanks to his electric pace, dribbling and creativity, and he would be difficult to replace.
For Courtois, the situation is even more pressing, as he could be the subject of cut-price offers in the summer if he has not signed a new deal at the club by then, and as one of the world's elite goalkeepers replacing him would be similarly tricky.
Hazard's comments will no doubt come as a relief to Chelsea fans, but speculation over Courtois and the former Lille man's future will likely continue until the deals are signed.