The 26-year-old Belgium international was granted an extended rest after his country finished third at the World Cup, but he was scheduled to return to training following Chelsea's 2-0 loss to Manchester City in the Community Shield.
Courtois joined Chelsea from Belgian side Genk in 2011 and spent the next three seasons on loan at Atletico Madrid before dislodging Petr Cech as first choice at Stamford Bridge.
He has repeatedly stated his desire to move closer to his two children in the Spanish capital, and with just a year remaining on his contract Chelsea risk losing him for a reduced fee in January or for free next summer.
Eden Hazard, whose deal expires in 2020, has also long been the subject of speculation over a move to Real, but the forward was present at the club's Cobham training base on Monday.
Chelsea boss Maurizio Sarri, who replaced Antonio Conte last month, admitted on Friday he was unsure whether Courtois would stay.
"At the moment Courtois is the goalkeeper of the club, of Chelsea," Sarri said. "I don't know in the future. It depends on the club. It depends especially on him, I think.
"But, I hope that Courtois will be our goalkeeper. It's very important for us to keep the top players."