Courtois has been Chelsea's No 1 goalkeeper for the past three seasons.
He successfully ousted Petr Cech from the side as the side last won the title in 2015.
However, he has been linked with a return to Spain regularly throughout his time at Stamford Bridge.
The Belgium international spent three years on loan in La Liga with Atletico Madrid, winning the title and featuring in a Champions League final.
Thibaut Courtois has reportedly asked his agent to force a move to Real Madrid
Real Madrid have given up on signing David De Gea
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And Spanish website Don Balon claim Courtois has demanded his agent force through a return to Spain.
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Real Madrid want to sign Courtois after giving up on Manchester United star David De Gea.
Current shot-stopper Keylor Navas looks set to leave at the end of the season after struggling for form.
Thibaut Courtois spent three years on loan at Atletico Madrid
Earlier this week it was reported Courtois had numerous reasons for wishing to return to Spain.
His family are still living in the Spanish capital and their daughter is set to be enrolled in a Spanish school.
And Courtois travels to Spain regularly to see them – and a permanent move to Madrid would allow him to see them more often.