The Spanish giants have long been linked with the Chelsea playmaker and Real boss Zinedine Zidane has spoken publicly of his admiration for the 26year-old.
Now, according to The Sun, they have firmed up their interest.
Talks are said to have already been held between Real chiefs and Hazard’s camp and a world record transfer bid is set to tabled.
The former Lille man has enjoyed an outstanding season for Chelsea, scoring 17 goals in 42 appearances, and played a pivotal role in their Premier League title success.