The 24-year-old moved to Stamford Bridge from Everton in January, but injuries limited his impact.
And although Chelsea would like to retain the services of the 26-year-old and risk losing him for free next summer, keeping an unsettled player could adversely affect the dressing room atmosphere.
Courtois was named best goalkeeper at this summer's World Cup in Russian Federation, where Belgium beat England in the third-place play-off.
Head coach Maurizio Sarri on Sunday, following the Community Shield loss to Manchester City at Wembley, said he would sanction Courtois' departure if the goalkeeper expresses a desire to leave.
"The future of Hazard, Willian (below) and the rest of the players defend on the club, not just me", continues Sarri.
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Citing 'sources close to the club, ' ESPN has claimed that the outcome of that meeting was Courtois telling Sarri that he wants to move on.
In particular, Sarri is facing a battle to keep hold of his goalkeeper Thibaut Courtois, after the Belgian was absent from training on Monday as he pushes for a transfer to Real Madrid.
Real Madrid have been monitoring Hazard for some time now and Chelsea would not like this to move forward any further.
Willian has insisted that he is happy to stay and fight for his place in the Chelsea FC first team under Maurizio Sarri.
Manchester City's pursuit of Jorginho faltered because Chelsea had a more pressing need for the Italy midfielder.
Chelsea vs Manchester City, Community Shield
Guardiola's men stormed to the Premier League title last season, with City breaking the 100-point barrier for the first time ever. Maybe it was a little bit late to announce that [he didn't want to join City] but if you decide you don't come, don't come.
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.
All that remains is for confirmation that Lerma has agreed personal terms, passed a medical and obtained a work permit.
They were joined by fellow World Cup participants Olivier Giroud, Gary Cahill and Michy Batshuayi ahead of Tuesday's International Champions Cup clash with Lyon.
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