Hazard has just a year left on his contract with Chelsea and the club face the prospect of losing their star player on a free transfer next summer.
The Belgian is keen to join Madrid, while Zinedine Zidane has made the 28-year-old his priority transfer target, as he plans to rebuild his squad.
Both clubs have not yet agreed a fee and the Spanish club have offered £86 million so far, which is below Chelsea’s asking price which is in excess of £110m.
Hazard is keen for his future to be resolved quickly and has told friends he wants the transfer to Madrid to be sorted by June 4.
The week after Chelsea’s Europa League final against Arsenal, Hazard will join up with Belgium’s squad, as they face Euro 2020 qualifiers against Kazakhstan on June 8 and Scotland on June 11.
