The 24-year-old moved to Stamford Bridge from Everton in January, but injuries limited his impact.
Courtois' Belgian teammate Eden Hazard has though been told he will not be leaving during this window, despite Real's interest in him. "I want only players with very high level of motivation", said Sarri, who has replaced Antonio Conte in charge.
Real Madrid themselves nearly closed a transfer for the Spanish stopper in January, although a disagreement between Zinedine Zidane and Florentino Perez ensured that such a deal wasn't able to go through, something which led to Kepa signing an improved contract with Athletic Club.
However Courtois, who is still on holiday after the Red Devils' run to the World Cup semi-finals, would not be drawn on his immediate future when quizzed by local media after the game. The only club I knew that made an official offer for me was Barcelona.
Thibaut Courtois has gone AWOL from training as the goalkeeper attempts to force an exit from Chelsea this summer, reports say.
"I have always been clear about enjoying playing for Chelsea, I have never (said) that I wanted to leave the club, but some situations that have happened with the other coach left me upset", said Willian.
David Luiz has urged Courtois and Hazard to stay, while insisting the Blues have enough quality even if the pair leave.
The Belgian global goalkeeper has just one year remaining on his deal with Chelsea and has been linked with a move to Real Madrid.
Well, we know where he stands now.
"I want them to stay, because we have top players with the confidence", Luiz said. "I hope this can be a year of victory for us".