The Belgium international has been linked with a move to the Santiago Bernabeu for some time and has previously expressed an interest in a switch to La Liga.
Hazard says the departure of childhood idol Zidane as head coach at the end of last season would not necessarily influence his plans, but has suggested he could still commit his future to Stamford Bridge.
"Would I like to sign for Real Madrid? Why not?" he told France Football. "I have never heard from Zidane and if he goes to Manchester United tomorrow, for example, I would not be there.
"Real Madrid without Zidane is different, but it is still Real Madrid.
"I've won everything in England, except the Community Shield, but that doesn't mean I'm going to leave. I've always said that I want to try something different after England, but there are things that might make me stay."
Hazard was initially tipped to leave Chelsea last season amid suggestions of a poor relationship with head coach Antonio Conte, who was replaced by Maurizio Sarri prior to the start of 2018-19.
The Italian has admitted that the club have been keen to extend the Belgian's deal at Stamford Bridge, that expires in 2020, saying that discussions have been taking place "every week".
Goal understands a five-year contract is on the table for Hazard if and when he decides to remain with the club, and that he'll become their highest earner on upwards of £300k per week.
The 28-year-old has been in impressive form this term, with 10 goals and 10 assists in 22 appearances in the Premier League, despite being used recently in a false nine role, one which he disliked playing under Conte.
10+ - Eden Hazard (10 goals and 10 assists) is one of two players in the Top 5 European Leagues to have both scored and assisted 10 or more goals in league play this season - the other is Lionel Messi (16 goals and 10 assists). Phenom. pic.twitter.com/5F1ZWFiYi5— OptaJoe (@OptaJoe) 12 January 2019
Hazard claims he has always been a source of frustration for his managers, however, and sees no reason why that will change regardless of the standard of his displays.
"I didn't only frustrate Conte," he said. "In my career, I've frustrated all my coaches. And here, Sarri, I still frustrate him. [Jose] Mourinho, I frustrated him.
"They think I need to score more, to do more here, more of that. The next one I have, I'll frustrate him, too."
Indeed, Hazard believes he may be different to the rest of the world's elite players as he is not obsessed with goals and silverware.
"I may be apart from the best players in the world. The best think goals, passes, trophies. I've never been like that. So, yes, maybe," he said.
"In professional football, there are a lot of players like me, who want to have fun."
However, the former Lille star still believes Lionel Messi and Cristiano Ronaldo must be considered a cut above the rest given their success over the last decade.
"I've been at their table for a long time!" he added. "Even if it's only been six months, I've had good form since the World Cup. I feel like that, even in the eyes of the fans.
"Before, in their eyes, it was: 'Yes, he's a very good player, but can he be among the greatest?'. But there is a moment where you have to keep your feet on the ground. For what they have done in the last 10 years, you can't be compared to them, it's impossible."