The 47-year-old – who spent four years at Stamford Bridge between 2007-2011 – insists Blues owner Roman Abramovich will not accept failure.
Sarri witnessed his side lose 6-0 against Manchester City at the Etihad as the West Londoners dropped down into sixth in the table.
And Clement told BeinSport, “There’s something going on that’s wrong behind the scenes.
“What I do know for sure is that the club will not accept that. The owner will not accept that.
“History shows that when the team is not playing at the level that is required, and expected for a club like that and what they’ve achieved over the years, they do take measures. They will act.”