The coach is clinging to his job after the 6-0 rout at Manchester City on Sunday, after which the Italian said he would welcome a chat with Roman Abramovich “because I never hear from him”.
Sarri has been given a stay of execution but faces a crucial 15 days.
Abramovich is out of the country but Stamford Bridge sources told Express Sport that if Sarri wants to talk to the Russian owner, there would be no problem.
Sarri took training as usual at the club’s Cobham headquarters yesterday.
“The coach and the players have to sort this out,” said the sources. “That is their job.”
Chelsea insist that Abramovich is not as trigger-happy as he once was, even though the axe could fall at any time in these next three weeks.
It is understood Sarri is also facing further scrutiny over his handling of youngster Callum Hudson-Odoi.
There is concern and unhappiness from above over his treatment of the starlet who Chelsea blocked from joining Bayern Munich last month.
Chelsea hoped Sarri would give him enough minutes to convince him to stay long-term, with his contract up in 2020.
But his game time has dried up since Chelsea chiefs dug their heels in and told Bayern once and for all that he would not be leaving in January.
Sarri apologised after Chelsea’s drubbing at City, with the Chelsea boss struggling to explain the Blues’ last three performances.
“In the last three matches away we’ve played very badly so we need to say sorry,” he said.
Chelsea captain Cesar Azpilicueta added: “It is one of the worst nights in my career.
“It is difficult to explain what happened.
“We are conceding a lot of goals and we cannot accept that. All I can do is apologise to the fans because it is not acceptable.”