The La Liga giants are intent on landing the Belgium international this summer.
And with Madrid preparing for life beyond Cristiano Ronaldo, Hazard is seen as a future Bernabeu star.
But squeezing him in to their team could prove tricky, with the likes of Ronaldo, Gareth Bale, Karim Benzema, Alvaro Morata and James Rodriguez all current options in attack.
Zinedine Zidane has his plan in place for Real Madrid next season
Hazard would be flanked by Luka Modric and Toni Kroos in behind
It is said Madrid will revert from their regular 4-3-3 set-up to a 4-1-2-1-2 formation.
And Eden Hazard would feature at the top of a midfield diamond.
Despite coming in off the left at Chelsea under Antonio Conte, the 26-year-old is versatile and can affect play in the centre.
As a result, Hazard would be flanked by Luka Modric and Toni Kroos in behind, with Casemiro in a holding role.
Real Madrid want Chelsea forward Eden Hazard to feature in the No10 role at the Bernabeu
La Liga stars who could join the Premier League
Mon, March 6, 2017
Get Quotes on Home Insurance
Express Sport takes a look at the star players who could swap La Liga for the Premier League
1 of 7
Antoine Griezmann (Atletico Madrid) – repeatedly linked with Manchester United
Ronaldo may lose his place as a regular member of Real Madrid's first XI with the arrival of Hazard
That would leave Gareth Bale as a first choice striker in a front two alongside either Ronaldo or Benzema.
Chelsea are reluctant to let Hazard go, but he is apparently seduced by the idea of having a new Madrid team being built around him.
The Blues ace could also be joined by team-mate Thibaut Courtois at the Bernabeu, as Madrid are keen to replace Keylor Navas with Chelsea’s goalkeeper too.