Before his move to Chelsea, Hazard was said to be a target for Los Blancos with Zinedine Zidane, in particular, being a big fan of Hazard.
The 26-year-old eventually moved to Stamford Bridge in 2012, helping the Blues most recently to a second Premier League title in three seasons.
However, the links to a move to Madrid have never subsided despite a fractured ankle resulting in the Belgian missing the start of the 2017/18 season.
The La Louvière native was also linked with a move to Barcelona following the departure of Neymar earlier this summer.
While he will stay at Chelsea for another season, Hazard, who returned from injury for Belgium during the international break, dropped a huge hint about potentially playing in La Liga.
"At the moment I'm good in England," he said in an interview with Marca. "I play in one of the best teams, but yes, the Spanish League is special."
"Why not one day? Of course, for the moment I'm here."
Hazard also spoke about Madrid in particular, touching upon why he believes they are the best club in the world while praising Zidane, who is now the manager at the helm.
"Well, I think now, at this moment, Real Madrid is the best team in the world," he explained. "They have won everything and have good players, a great coach. He [Zidane] has won everything both player and coach."
"He's a special type. Everyone knows him as a player. To think of football is to think of Zidane. As a player and as a coach, he has won everything and he is special, what he has achieved on and off the pitch has been magical and I'm so happy to see him succeed again."
Madrid became the first club to retain the Champions League in the modern era when they beat Juventus 4-1 in the final in Cardiff on 3 June and won another Uefa Super Cup following their 2-1 win over Manchester United on 9 August under Zidane.
Interestingly, Cristiano Ronaldo named the former Lille man as one of the players who could succeed him and take the throne in football.
Hazard himself, recently joked that he could be worth €300m (£276m, $357m) but that it would only be possible to know if he takes part in a transfer.