The Belgium worldwide, like his compatriot Eden Hazard, had been due on Monday afternoon at Chelsea's Cobham training base where the new head coach hoped to hold discussions over his future.
Sarri said he would sanction Courtois' departure if the goalkeeper expresses a desire to leave following Sunday's Community Shield defeat to Manchester City.
Chelsea's eagerness to halt Real Madrid's efforts to sign Hazard may lead to him being offered the chance to become club Blues captain, yet persuading Courtois and Willian to stay will be a tough task.
"If Courtois says the same to me, [then] I have to speak with my club, of course, because I want only players with a very high level of motivation".
And that leaves Chelsea in a race to land a new goalkeeper, with Stoke City's Jack Butland and Sevilla's Sergio Rico on their shortlist, before Thursday's transfer deadline.
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Chelsea winger Eden Hazard has also been linked with Real, but did attend training with the Blues on Monday.
Manchester City won the game 2-0.
Get the latest World Cup news updates. "But I am quite calm and hope for a good outcome".
"Chelsea wants for the best players to stay", said Luiz. "That is behind me now, and I'm feeling strong and ready to go". "Everybody has the opportunity, you just have to show him character, physical quality, technical quality, so since the first day I'm trying to do that".
The possibility of Willian ending his five-year spell in west London had looked more likely following the breakdown in his relationship with former manager Antonio Conte.
"My mother played football so I learned a lot from her", Jorginho told reporters.