The 27-year-old has two years left on his current deal and the west London club are hopeful of agreeing new terms.
Hazard is in the form of his career, with seven goals in eight games in the Premier League this season so far.
Chelsea are level on points with Manchester City and Liverpool at the top of table as it stands.
Real Madrid have been rumoured to be interested in Hazard recently, and it seems the interest is at least partially reciprocated.
After scoring his eighth goal of the season in all competitions in the 3-0 win at Southampton on Sunday, Hazard admitted he was torn between his dream of playing for Real or sticking at Stamford Bridge.
"Sometimes in my head, I wake up in the morning and think I want to go. Sometimes I think I want to stay," he said.
"It is a hard decision. It is my future. I am 27 and will turn 28 in January.
"I want what's good for me but I want what's good for the club because the club has given me everything.
"I don't want to say 'yes I am signing a new contract' and then in the end I don't end up signing. So I will see."