The Belgian forward, 26, was back to his best last season as Chelsea romped to the Premier League title, after a sub-par season before in which he struggled for goals.
He has continued his impressive performances in 2017-18 and, although his contract runs until June 2020, rumours have continued to swirl regarding a potential transfer to the Santiago Bernabeu.
Hazard's father, Thierry, confirmed his son is playing a waiting game with his Chelsea contract in an effort to keep the door ajar to Zinedine Zidane's side.
"What I can reveal about Eden is that he refused a contract extension," he told Le Soir.
"This was so that, if necessary, he could follow the interest of the Real, whom he could see himself playing for.
"But, as of right now, there is no contact from Real Madrid. Eden is only one of the parties involved in his future."
Hazard has been candid about his interest in playing for the reigning European champions in recent months, saying in November that "everyone knows the admiration I have for Real Madrid".
The former Lille winger has scored eight times for Antonio Conte's side this season, assisting a further eight times across all competitions.