The Blues’ 2-0 defeat to Manchester United on Monday night was the club’s third loss in their last five games.
And things don’t look like they will be getting any easier with the London club’s next fixture coming against City again in the Carabao Cup final on Sunday.
Sarri’s job now remains in further jeopardy following such bad results, with the club already obtaining a history of quick dismissals.
The Blues have had 11 managers over the last decade, with Antonio Conte lasting just two seasons before he was shown the door.
Despite a decent start to the campaign, poor results have intensified the speculation regarding Sarri's long-term future at the club and Sutton believes the Italian will be next on the list of sacked managers.
"This is Maurizio Sarri's last game at Chelsea. The Italian job is over for them," Sutton told BBC 5 Live. "He's done. Sarri-ball is broken.
"The Chelsea owner will be thinking, 'Will we get top four? Can I go to the Manchester City game with confidence?' Absolutely not.
“Is he going to chuck all his eggs in the Europa League basket with a manager who can't motivate his players? No.
"History tells us the Chelsea owner doesn't mess about."
Sarri was only appointed as the club’s manager back in July 2018, and is contracted to remain in charge until 2021.
He is still yet to win a trophy as a manager, with this weekend’s Carabao Cup potentially his first ever silverware.
Following Sunday’s meeting with City at Wembley, Chelsea then face Spurs on February 27 before a trip to Craven Cottage to play Fulham on March 3.