The Daily Mirror say the Blues stopper is Real’s top target this summer.
Zinedine Zidane is desperate to sign a new No.1 – with Manchester United star David De Gea also being considered.
“Chelsea will have to give Thibaut Courtois more than £200,000-a-week to stop him from joining Real Madrid”
Real believe Courtois – who spent three years in La Liga during his time at Atletico Madrid – could be tempted with a return.
The Belgium international is under contract until 2019 and Chelsea boss Antonio Conte is desperate to keep his star man.
The Mirror add that Courtois knows he’s wanted and the Blues face a huge battle to stop him from leaving.
They say his contract will have to be worth more than £200,000-a-week.
The goalkeeper has impressed at Chelsea this season, helping them to a 10-point lead at the top of the Premier League table.