Hazard, who led Belgium to 3rd place at the 2018 World Cup, feels it's the right time for a fresh challenge with Madrid as his preferred location.
The Belgian was crowned the second best player at the World Cup, and after leading his country to third place in Russia, stated he felt the time was right for a fresh challenge with Madrid his preferred destination.
"I spoke after the World Cup and I said that I think it is time to change because I played a great World Cup," Hazard told the British media after scoring in Sunday's 3-0 victory at Southampton.
"I am really in the game, I am playing good football at the moment. Real Madrid is the best club in the world. I don't want to lie today. It is my dream since I was a kid. I was dreaming about this club. We will see. I don't want to talk about this every day. I don't have time but we will talk about my future soon," he added.
Madrid could do with Hazard's firepower in the absence of the departed Cristiano Ronaldo, having failed to score in four consecutive games for the first time since 1985.
Hazard is out of contract in 2020, but doesn't want to follow the example of international team-mate Thibaut Courtois in forcing his way out of the club.
Courtois had just a year to run on his contract, lowering his transfer value, when he refused to return to pre-season training with Chelsea before sealing a move to Real in August.
"I don't want that," Hazard said. "I want what's good for me, but I want what's good for the club because the club has given me everything.
"I don't want to say: 'Yes, I am signing a new contract' and then in the end I don't end up signing. So I will see.
"Sometimes in my head, I wake up in the morning and think I want to go. Sometimes I think I want to stay. It is a hard decision. It is my future. I am 27 and I will turn 28 in January."
Madrid have won the Champions League for the past three seasons, while Chelsea failed to even qualify for Europe's premier club competition this season after finishing sixth in the Premier League.
However, Hazard insisted it is not trophies, but the enjoyment he gets from his football that will be the determining factor in his decision.
And he is thriving in Sarri's more expansive set-up after two seasons under the more cautious approach of Antonio Conte.
"It is not trophies. Of course, when you play, you want to win," added Hazard. "But I just want to enjoy things on the pitch, like I am at the moment. Then I am happy."