Los Blancos have been keen to make a move, but thus far the Blues have refused to budge on their £40 million (€45m/$52m) valuation of the player.
While no deal is in place, manager Maurizio Sarri did not appear confident on Friday that the Stamford Bridge will be able to retain their No.1, while former Belgium coach Graeme Jones says that a move is "definitely" on the cards.
“I have been reading everywhere that Chelsea are saying it is up to Thibaut, but he has made it clear to the club that the best option for him is to move to Madrid,” Christophe Henrotay said, according to The Sun.
“For him this is a big decision because he wants to be near his family, and there is an offer in place for Chelsea to accept.”
Some supporters have criticised the 26-year-old as they feel that his desire to move to the Bernabeu is being financially driven, but Henrotay has dismissed those claims out of hand.
“We have seen suggestions that it is about money, and it is true he could get an increase with a move.
“But he has turned down a better offer elsewhere because this is more than a financial decision.
“Throughout this it has important for everyone to be reasonable, and the buying club has come up with a reasonable offer for a player who has one year left on his contract when they know they could sign him without a fee in 12 months.
“Chelsea could get a fair fee for him now and sign a replacement. Or they would still have to sign a replacement next summer, but without getting a fee for Thibaut.
“It is understandable people might be upset because he wants to leave the club, we accept that.
“But this is a human decision based on someone wanting to be close to his children - and that is a reasonable thing too.”
With the English transfer window set to shut next Thursday, time is running out for Chelsea to find a replacement should they decide to sell.
Meanwhile, Courtois is expected to report back to training on Monday, just five days before Maurizio Sarri’s side begin their Premier League campaign with a fixture against Huddersfield Town.