Courtois has only 12 months until his current deal expires at Stamford Bridge, and he has expressed a desire to return to Madrid, where his children live.
Speaking after Belgium's World Cup third place play-off win over England on Saturday, Courtois was coy on the subject of his future.
According to the Belgium press, Courtois is very close to joining Real Madrid after his positive performances in the World Cup. According to Het Laatste Nieuws, Courtois will get a €13M annual gross salary. It will be announced shortly after the World Cup. [marca] pic.twitter.com/4sgVhx6nVd— SB (@Realmadridplace) July 14, 2018
"Now I'm going to talk to my agent to see what the possibilities are," said the goalkeeper, quoted by Marca. "All options are open for me. I may also stay at Chelsea.
"People always complain that players don't comply with their contracts, but maybe they do. I don't think they will keep someone with my qualities on the bench, even if I don't sign [a new contract].
"But maybe [staying] is possible, because I like it in London."
Asked to more directly rule out a move to Real Madrid, Courtois responded with a definitive "no."
Courtois played in Madrid for Real's rivals Atletico for three seasons between 2011 and 2014, when he was on loan from Chelsea.
His children, born in 2015 and 2017, live in the city with their mother and Courtois has spoken about the heartache of being separated from his family for so long.
"My kids are the most important for me," he said earlier this month. "I haven’t seen them a lot in the last 18 months. Facetime is nice, but seeing them grow up is something different. My kids will play an important role in my decision."
Courtois played every game for Belgium at the World Cup as they recorded their highest ever finish at the tournament.