The shock reports coming out of Spain claim the Belgian wants a move to the Bernabeu this summer.
Hazard has been in fine form this season, netting 15 times and providing nine assists in all competitions.
And Diario Gol report the 27-year-old is in talks with the La Liga champions about a switch.
Chelsea and Real Madrid are said to be negotiating a blockbuster summer deal which would see Hazard leave Stamford Bridge.
And the forward has told current team-mate Morata in order to push through the transfer he is pushing for Isco to join the Blues.
Paris St-Germain – 25/1
The Spanish midfielder is reportedly unhappy with his amount of playing time and could be tempted by Chelsea.
There is also said to be tension between Isco and Zinedine Zidane as well as top stars Cristiano Ronaldo and Karim Benzema.
Real Madrid president Florentino Perez knows he has to offer a star to secure the signing of Hazard and has opted to include the midfielder as a result.
Chelsea are more interested in Marco Asensio but Los Blancos are keen to keep the forward at the club.
In fact they rejected an approach from Liverpool last month.
Hazard was in superb form last night, scoring twice as Chelsea beat West Brom 3-0 at Stamford Bridge.
The Blues return to action on Friday when they host Hull in the FA Cup fifth round.