Hazard was tipped to leave Stamford Bridge in the last transfer window after admitting in July he was tempted to try "something different".
However, the Belgium star later said he was happy to stay and has been in superb form this season, netting a stunning Carabao Cup winner against Liverpool and leading the Premier League scoring charts with seven goals in eight appearances.
Chelsea is understandably keen to extend its prized asset's current deal, which runs out in 2020, but Hazard suggested the lure of LaLiga giant Madrid might be too much to turn down.
Speaking after Chelsea's 3-0 win over Southampton on Monday (NZDT), in which he scored the opener, he said: "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.
"It is also when you have a dream and you want to make it happen.
"It is like I have said a lot of times; if I leave I will be happy. I know if I stay, I will be happy. It is not like if I go I am happy and if I stay that I am unhappy.
"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 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."
Hazard, who is included on the Ballon d'Or shortlist, will hope to maintain his blistering start to his club season when he links up with Belgium this week ahead of a Nations League clash with Switzerland on Friday.