Chelsea and Newcastle United are among the English teams that have been alerted to the possibility of signing the 30-year-old.
Hazard failed to come off the bench for last weekend’s El Clasico win over Barcelona.
ALSO READ: Chelsea open to re-signing Hazard
After the game, manager Carlo Ancelotti admitted that “the problem [Hazard] has right now is he has a coach who prefers another player.”
The Belgian was signed from Chelsea in 2019 for a deal worth an initial €100 million with a series of performance-based add-ons.
Hazard has started just 25 games in LaLiga and has five goals from 52 appearances across all competitions, with his time in Spain plagued by injuries.
Madrid are looking to raise funds to pursue Borussia Dortmund’s Erling Haaland next summer and also land Paris Saint-Germain’s Kylian Mbappe, who will potentially be available on a free transfer.