MailOnline's Harry Slavin noted Madrid-based newspapers Marca and AS had stories about the Belgian on their front page, and the latter said he is already on the hunt for property.
On Tuesday, RMC (h/t Get French Football News) reported an agreement has already been reached between the Blues and Los Blancos.
Per AS' Ignacio Camacho, Courtois already owns property in Madrid, where his two children live with his former partner.
Courtois previously lived in Madrid between 2011 and 2014, when he played for Real's local rivals Atletico Madrid. Earlier this year, he told Sport/Foot (h/t James Benge of the Evening Standard) how he missed his kids and wanted to return to the capital:
"My personal situation is related to the city of Madrid. My two children live there with their mum. I have my daughter every day on FaceTime. She often tells me that she misses me. My son is still too small to communicate like that.
"Whenever I have the opportunity, I try to return to Spain. As a situation, it is not always easy. Yes, my heart is in Madrid. It is logical and understandable."
With just one year left on his contract, the 2018 FIFA World Cup Golden Glove winner will be available for a bargain fee of just £36 million, according to Slavin. That's exceptional value for Los Blancos, who have long been linked with several goalkeepers as they look to add competition for or upgrade on Keylor Navas.
The 26-year-old's move seems only a matter of time, with reports the Blues are already looking at replacements:
While plenty of fans will be disappointed to see the stopper go, this move has felt inevitable for some time. Courtois never fully shut the door on speculation and openly professed his love for the city of Madrid and desire to return one day.
With just one year left on his deal, the Blues have to make this move now, as they're unlikely to reach an agreement on new terms if they don't.
According to the Mirror's David Anderson and Adrian Kajumba, the Blues will do everything in their power to beat Liverpool to the signing of AS Roma's Alisson Becker. Asking for Navas in a swap deal could be another option.