The versatile attacker has been a big hit since his mega money 2012 switch to West London from Lille, and has developed into one of the Blues’ key men in recent times.
His consistent displays have caught the eye of Real, who are ready to mount a serious move for his services next month.
The Madrid giants were believed to have made Liverpool’s Luis Suarez their top target, but his recent contract extension appears to have scrapped any potential move to the Bernabeu during the next window.
Although not a direct alternative to the Uruguayan, Los Blancos are believed to see Hazard as a top addition to their attacking armoury.
Chelsea are, naturally, far from keen to let the 22-year-old move on, but Real could look to tempt Jose Mourinho to sell by offering Angel Di Maria as a makeweight.
The Spaniards are also watching Hazard’s team-mate Ramires, who is seen as a possible solution to their current midfield issues.