The Spanish giants have been linked with a move for the Blues’ stopper in recent times amid speculation that they’re switching their attention away from Manchester United’s David de Gea.
The European champions are thought to be keen to replace club icon Iker Casillas with a genuine world class No. 1, with the experienced Los Blancos man having suffered a dip in form.
However, any hopes of landing Courtois may hinge on allowing Varane to head to west London in exchange.
The 21-year-old is thought to be a target for Chelsea, with a deadline day swoop having been mooted.
Jose Mourinho coached him while at Real and has already hailed him as one of the best young centre-backs on the planet.
Courtois only recently broke into the Premier League leaders’ first team after an extended loan spell with Atletico Madrid.