Courtois is open to a return to Madrid, with his wife and child living in the city after he previously spent three years on loan in the Spanish capital with Los Blancos' rivals Atletico to gain experience.
Chelsea want to keep Courtois but they could be forced into selling him, if their number one keeper pushes for a move. Any deal will likely break the transfer record for a goalkeeper, which is still Gianluigi Buffon's £47.5 million switch from Parma to Juventus in 2001.
Madrid are keen to make a statement by signing a world-class goalkeeper and see Courtois as a more realistic option than Manchester United's David De Gea, who they failed to sign back in 2015, as they look to improve upon current number one Keylor Navas.
The European champions have also outlined Tottenham's Hugo Lloris and AC Milan's Gianluigi Donnarumma, but Courtois is a very strong preference. Madrid want to show their intent after losing more games in a month-and-a-half of 2017, than in the whole of 2016.
Navas remains keen to stay at Madrid, despite talk of a high-profile signing coming in to compete for the number one shirt at the Bernabeu.
"They always bring the best players in the world here [to Madrid]," Navas said at the start of February. "That motivates me [news of potentially signing Courtois] as it means that I am here among the best. I know there are many things out of my control, but I will fight hard for the things that I can control.
"I want to be here for many years. I am relaxed about it all. I would love to retire here at Madrid. To be here is a blessing, a privilege and a responsibility."
Oblak will be a costly replacement for Courtois after he signed a new deal in February which includes a €100 million release clause. Atletico could make a big profit on Oblak, who was signed from Benfica in a €16 million deal in 2014 after Courtois returned to Chelsea.
Asmir Begovic could also leave Stamford Bridge in the summer after his January transfer deadline day move to Bournemouth collapsed as Chelsea failed to replace him with Celtic's Craig Gordon.
Begovic said that he has put transfers to the back of his mind as Antonio Conte picks him in the FA Cup, but he is likely to take another look at options in the summer, with Bournemouth still interested in him.