The Blues stopper is wanted by the La Liga champions to replace Keylor Navas at the end of the season.
That’s after Real president Florentino Perez chose to give up on Manchester United ace David De Gea and put all his efforts into signing Courtois instead.
Spanish outlet Diario Gol say Courtois has an agreement in place with the club to move at the end of the season.
Real are also expected to sign Kepa Arrizabalaga from Athletic Bilbao as they completely overhaul their goalkeeper ranks.
Courtois has been in fine form again this season, keeping 11 clean sheets in the Premier League to date.
