Courtois has been a huge success with the Blues since finally arriving at Stamford Bridge in 2014, with 118 appearances being made in all competitions since the Belgian stopper ended a loan spell with Atletico Madrid.
However, according to Marca, the 25-year-old enjoyed his time living in the Spanish capital and that has led to ambitions of a future transfer to the reigning Champions League winners.
Courtois is allegedly happy with life in London and remains grateful for the Blues spending £5m on his signature when he was just 19, but it has been suggested that personal reasons are behind his desire to return to Spain.
Real have frequently been linked with a move for Manchester United stopper David de Gea but as long as that potential deal remains up in the air, Courtois is seemingly prepared to bide his time before making a final decision over his next career move.
Courtois has just under two years remaining on his existing contract with the West Londoners.