Hazard, 27, has starred for the Blues since his £31,5m (R514m) move from Ligue 1 side Lille in 2012, featuring four times in the PFA Premier League Team of the Year, winning two Premier League titles, the EFL Cup and the UEFA Europa League.
Now, as he enters his peak, Real have made their interest known in the Belgium international, who's scored 15 goals and registered nine assists in 36 games for Antonio Conte's side this season.
"I still have 2½ years on my contract," he told reporters, as quoted via KweseESPN. "I'm very settled here and playing every game. The fans like me a lot and my family likes it here.
"It's been several years now they're interested - when it's not Real, it's Paris, when it's not Paris, it's Real. I'm happy where I am."