The 26-year-old Belgium international, linked with a move to Real Madrid, was granted an extended rest after his country finished third at the World Cup, but did not turn up for training on Monday.
The Sun newspaper reported on Tuesday that he would miss training for a second day as the impasse continued.
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.
Second-choice 'keeper Willy Caballero played in goal on Sunday as Chelsea lost 2-0 to champions Manchester City in the Community Shield.
The Times said Chelsea had indicated they would accept his request for a transfer after a £35 million offer ($45 million) from Real if they could secure a replacement in time.
The Premier League's transfer window shuts at 1600 GMT on Thursday, heaping pressure on Sarri.
The Times said Chelsea had turned their attention to Stoke City's Jack Butland after Everton made it clear England goalkeeper Jordan Pickford was not for sale.
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.