Maurizio Sarri's coaching staff are convinced that they will be heading for the Stamford Bridge exit at the end of the season.
The Italian manager has struggled to win the Blues fans over during his first season as Chelsea manager and his stay may be cut short if his woes as boss continue.
According to The Sun, Gianfranco Zola and Co are openly talking about being axed once the season has concluded this summer.
Sarri lost his cool during Monday night's encounter with Burnley after he was sent to the stands late on in the game.
While Chelsea can still qualify for the Champions League, it may not be enough to keep the Italian at the club for another season.
Following the club's bust-up after their 2-2 draw, Chelsea and Burnley will face no further action from the Premier League or Football Association following a melee between the two benches at Stamford Bridge.
Sarri had already been fined £8,000 after he admitted a misconduct charge for the incident but both teams have escaped further sanctions following discussions.
The game finished 2-2 as Chelsea's top four hopes were dented. But the final flashpoint came in the 94th minute when the Italian boss was sent off by referee Kevin Friend.
Sarri was sent off by referee Kevin Friend after leaving his technical area to dispute a late decision.
His dismissal sparked skirmishes and confrontations between coaches on the rival benches which recurred at the final whistle when Burnley's goalkeeping coach Billy Mercer featured heavily.
Chelsea complained to the FA after the game that a member of Burnley's coaching staff had referred to Sarri as a 's*** Italian'.
The west London club were initially irate at suggestions Burnley would face no further punishment for their role but both sides have reached an agreement and can move past it.
In a statement on both club's social media channels on Thursday night, they said: 'Issues arising between both benches during Monday night’s match have been resolved between the coaches and clubs, and a line has been drawn under the matter.'
No punches were thrown but plenty of insults did hit the target and Chelsea were furious about what they saw as a deliberate attempt to wind-up Sarri.
'Maurizio felt very unhappy,' Zola said after Monday's game as he took on Sarri's media responsibilities.
'He's very frustrated. We understand it's a football game. You say words because of the adrenaline, but he wasn't particularly happy. If Maurizio said that, probably it's something that could have been avoided.'