The Belgian is widely considered to be one of the best goalkeepers in world football, but with his contract set to expire in 2019, his current employers are keen to tie him down to a new deal.
The goalkeeper is well aware of his status as one of the world's best and is hoping that he will be rewarded with a mega-money deal.
However, Real Madrid are thought to be following developments closely, with the 25-year-old well versed in life in the Spanish capital, having spent three years on loan with Real's city rivals Atletico earlier in his career.
Despite the impressive recent form of Keylor Navas, Real are thought to be on the look out for a long-term option between the sticks, hence their interest in AC Milan's Gianluigi Donnarumma earlier this summer.
As is the norm these days, talks over a new deal for Courtois started some time ago and with the player now into the last two years of his contract and with talks over a new one hitting the buffers, the 'Blues' may be forced to sell the player in the summer in order to avoid losing him on a free when his contract expires.
Madrid are well aware of this and are hoping to take advantage to allow the Belgian to follow in the footsteps of Gareth Bale and Luka Modric in swapping London for Madrid.