The 28-year-old had hinted at an exit from Stamford Bridge following the 2018 World Cup, when he said: "It might be time to discover something different" -- while, earlier in this campaign, he said playing for the Real Madrid was his "dream."
Hazard, whose Chelsea contract expires in 18 months' time, has been in England since 2012 and won every major domestic honour available to him.
"Why not?" he said when asked if he would be happy to move to Real Madrid. "I've seen all there is to see.
"I've won everything here: the two cups, the league, apart from the Community Shield, but that doesn't mean I am going to leave.
"I have always said that, after England, I wanted to discover something else. But there are things that could make me stay too. I'm not far off the peak of my career, that's sure.
"Even if things can always be better, that's for sure too. I am at a crossroads, yes. We are going to take the right turn."
Hazard has scored 10 goals and contributed as many assists in 22 Premier League matches this season; and he said he has "the same footballing ideas" as Chelsea boss Maurizio Sarri.
"He's close to the game. The coaches before were perhaps a bit less so," Hazard said. "For them, it was more important to win, to defend well. Even if, for him too, you have to defend well. Training sessions aren't easy, we go over the same things a lot. But once out there on the pitch, for 90 minutes, he wants us to have the ball."
Meanwhile, Sarri held a meeting with his players on Tuesday morning to address recent issues following Saturday's 2-0 defeat to Arsenal which led to the ex-Napoli boss accusing his players of being "not particularly aggressive from the mental point of view."
ESPN FC's France correspondent Ian Holyman contributed to this report