Hazard's form so far this term has once again drawn comparisons to some of the world's best players, with the Belgian having scored eight goals and set up a further four across all competitions for the Blues.
Madrid president Florentino Perez is understood to be lining up a number of possible high-profile transfers over the next two windows, having seen his side fall 11 points adrift of La Liga leaders Barcelona ahead of the first El Clasico of the season.
Spanish media outlet Diario Gol now claims that the European champions are already in advanced talks with Hazard over a potential switch, although any move is unlikely to take place before next summer's World Cup in Russia.
Madrid manager Zinedine Zidane is known to be a keen admirer of the winger and has reportedly told Perez that he wants him at the club.
However, the reports goes on to state that Marco Asensio has given Madrid an ultimatum over their pursuit of Hazard, telling Los Blancos that he will leave the club if Hazard arrives.