Hazard is said to have raised concern among the Los Blancos coaching staff after reportedly returning from the international break in a poor physical condition.
The 29-year-old, who joined Real from Chelsea in a club-record deal last season, played no part in either of Belgium's UEFA Nations League matches despite being called up, with manager Roberto Martinez admitting the player was not in the right condition to feature in either fixture.
"Medically he's absolutely fine, it's just a question of being careful when bringing him back in," Martinez told Cadena Cope.
"He's still not 100% and hasn't been able to take part in group training at his club. We're going to be very careful and not run any kind of risk. Eden needed to work on his own to be able to start pre-season without any risks. He's not ready to play 90 minutes."
Spanish publication Diario Sport has claimed that Los Blancos are unhappy that Hazard joined up with his international teammates instead of working on his fitness in Madrid, and that the former Blues star will need three to four weeks of conditioning before being at the required fitness.
Hazard's reported indiscretion comes just a year after he arrived at the Santiago Bernabeu 7kg overweight, and is said to have raised question marks about his commitment to the club.