Belgium sealed a third-place World Cup finish with a 2-0 win over England.
And after the match, Hazard told reporters he is strongly considering his Chelsea future.
“After six wonderful years at Chelsea it might be time to discover something different,” he told Belgian outlet HLN.
“Certainly after this World Cup. I can decide if I want to stay or go, but Chelsea will make the final decision – if they want to let me go. You know my preferred destination.”
The destination Hazard hinted at is Real Madrid and the Champions League winners are on the hunt for a replacement for Cristiano Ronaldo.
Courtois has also been heavily linked with a move to the Bernabeu, which would allow him to reunite with his two children.
And when asked about his own future, the 26-year-old said he wants to continue playing with Hazard.
Courtois said: “Wherever I go, Hazard must come along. We will not let each other go. We’ll see. Now first vacation. And agree with my entourage in between.”
But Courtois also made clear that he could still stay at Stamford Bridge once he has spoken to new boss Maurizio Sarri.
He said: “Now I’m going to talk to my manager to see what the possibilities are.
“All options are open to me. Also stay at Chelsea, yes. People always complain that players do not comply with their contracts, but maybe I will.
“I do not think they will keep someone with my qualities on the bench, even if I do not sign. But maybe that’s possible because I like being in London.”