The Belgium international is facing an uncertain future at the west London side given the shot stopper has less than 12 months on his current deal.
Courtois has failed to reach an agreement with the Blues over a new deal despite Chelsea FC offering the Belgian a lucrative new contract.
The 27-year-old has been regularly linked with a move to La Liga duo Atletico Madrid and Real Madrid over the past few seasons.
Courtois’ ex girlfriend and two children are still in the Spanish capital to partly explain the links to a return to Madrid.
Current Chelsea FC boss Antonio Conte is facing an uncertain future at the west London side after a fifth-placed finish last term.
Ex Napoli head coach Sarri is widely tipped to take over the reins from his compatriot in the summer.
Sky Sports News reporter Warren warned Sarri that he will have to tackle the urgent situation involving Courtois.
“One of the first items for Sarri at Chelsea would be to sort out the goalkeeper situation,” Warren told the Transfer Talk podcast.
“Courtois’ future is still in doubt. Once again, the speculation is that he could be off. He has one year left on his contract and he is yet to sign a new deal.
Chelsea FC won the Premier League title in two of the past four seasons under Jose Mourinho and Conte.
The Blues were 1-0 winners against bitter rivals Manchester United in the FA Cup final at Wembley last term.
MORE: Man United latest news
MORE: Arsenal latest news
MORE: Chelsea latest news
MORE: Liverpool latest news