The Spanish side have been courting the 2018 World Cup Golden Glove winner and have made a lucrative offer as they look to facilitate a switch from Stamford Bridge to the Santiago Bernabeu.
Recent reports claim the Champions League holders have already agreed personal terms with the towering star but are yet to agree a deal with the Blues.
According to Daily Record reporter Ian McGarry, the Belgian's move to Real is 'inevitable', while Leicester City's Kasper Schmeichel is his most likely replacement.
“It is inevitable Courtois will move to Real Madrid,” McGarry said on the Transfer Window podcast (H/T The Sport Review). “Schmeichel is the most likely replacement.”
The Londoners have also been linked to former Liverpool stopper Pep Reina, while Petr Cech - a Chelsea legend - is rumoured to be a target as well.
The veteran glovesman has since moved to dismiss the talk of a return to the Bridge, however.
"I have a contract with Arsenal,” he said, as quoted by Goal. "I am concentrating on this season, on the competition between the goalkeepers because we have plenty of options.
"I’m doing my best to show to the manager that I can be in the starting lineup when the season starts. That’s my aim and as for the speculation, I don’t really follow it. I’ve had no contact with Chelsea."
Schmeichel, meanwhile, rose to stardom during Leicester's title-winning campaign and has retained his status as one of the best shot-stoppers in the Premier League.
Whether or not he moves to Chelsea remains to be seen, but the Blues would do well to secure the services of the talented Dane if they do lose Courtois this summer.
In the meantime, though, they have signed former England keeper Rob Green as a backup.