The Daily Mail says Fabregas caused controversy and invited criticism online as the latest news regarding Conte circulated when he liked a tweet celebrating the development.
However, the Spaniard moved quickly to set the record straight, replying to the initial message: "Pressed by mistake. Sorry."
That apology now appears to have been deleted.
He then followed it up by thanking Conte for putting faith in him after originally being left out in the cold.
Fabregas wrote: "Thank you Mister for another Premier League title and FA Cup. It wasn't easy for me to convince you in the beginning but in the end I hope I did you proud! Good luck for the future. #CFC."