The European champions have long been linked with a move for Hazard and were understood to consider the Belgian a potential replacement for Cristiano Ronaldo, who could leave the club at the end of the season.
Hazard reportedly rejected a new Chelsea deal in order to lure an approach from Madrid, but Spanish publication Marca claims that Los Blancos have instead cooled their interest.
The report says that the club's board believe Asensio has the potential to be as good if not better than Hazard, and are worried that signing the 26-year-old would inhibit Asensio's progress.
Madrid have also been increasingly linked with Paris Saint-Germain winger Neymar, who they are believed to see as a more viable long-term replacement for Ronaldo than Hazard.
Hazard has scored eight goals and created four more in 25 appearances for Chelsea so far this season.