The 23-year-old has established himself as one of the world's best 'keepers and, as a result, emerged a transfer target for Europe's elite.
Reports claim Real have the Belgian firmly in their sights amidst their bid to find a long-term replacement for the recently-departed Iker Casillas.
SIGN UP NOW
Want to become a GMS writer? Sign up now and submit a 250 word test article: http://gms.to/haveyoursay4
Los Blancos still intend on making another approach for Manchester United's David de Gea despite having failed in their pursuit of the shot-stopper last summer.
And should they fail once again to lure the Spaniard to the Bernabeu, Courtois would certainly prove an able alternative. The question remains, however, of whether manager Zinedine Zidane could persuade Chelsea to part with their towering 'keeper.
Courtois is said to be interested in a future return to La Liga having already spent a highly successful three years on loan at the Vicente Calderon with Atletico Madrid.
Perhaps worringly for Chelsea, their struggles this season and imminent failure to secure a place in the Champions League could hold a damaging effect in their bid to keep hold of their key players at Stamford Bridge.
Teammates Cesc Fabregas, Diego Costa and Eden Hazard have also been linked with summer moves away from west London, the latter a target for Real too.