This is according to the Telegraph, who have exclusively revealed that Courtois was Real Madrid's first option - ahead of Manchester United goalkeeper David de Gea - but the Spanish giants were scared off from making a formal move for the 23-year-old after hearing Chelsea's staggering demands.
Real Madrid were prepared to make Courtois the most expensive keeper in history by paying £37 million, but Chelsea told them to double that fee to stand any realistic chance of signing the player.
Los Blancos, subsequently, are attempting to wrap up a deal for De Gea and could announce his arrival as early as next week.
United are reportedly braced for Real Madrid to step-up their pursuit of De Gea once he returns from Spain's Euro 2016 qualifier against Belarus on Sunday.
De Gea set to replace Casillas
Reports in Spain, meanwhile, claim Iker Casillas has reached an agreement with Real Madrid to leave the Bernabeu this summer.
The 34-year-old will lose his first-team place once De Gea signs, while Manchester United manager Louis van Gaal must decide whether to make moves for either Petr Cech or Hugo Lloris, or stick with Victor Valdes heading into the 2015-16 campaign.
Courtois is arguably better than De Gea
Even if Real Madrid had offered Chelsea an astronomical fee for Courtois, Jose Mourinho would surely have been tempted to reject it.
Courtois is arguably already the world's best goalkeeper - ahead of both De Gea and Bayern Munich's Manuel Neuer - and is currently on course to develop into one of the best of all time.
The 6ft 6in shot-stopper was magnificent during his three-year loan spell with Atletico Madrid, winning a host of team and individual honours, and won the Premier League and Capital One Cup in his first proper season at Stamford Bridge.
Chelsea would not have been able to recruit a better replacement - and there's every chance the man who replaced Petr Cech at the start of last season will retain his place in the Blues' first team for the next 10-15 years.
Perhaps Real Madrid will regret not paying the money later down the line, although in the form of De Gea they are signing a world-class alternative of similar quality.
Is Thibaut Courtois a better goalkeeper than David de Gea? Have your say in the comments below!