The 31-year-old is out of contract at the end of the season and Sky sources understand Chelsea and Monaco are close to agreeing a deal for the midfielder to move to Ligue 1 in January.
Fabregas is expected make his final appearance for the Blues on Saturday when Nottingham Forest visit Stamford Bridge in the third round of the FA Cup.
Fabregas has struggled for first-team opportunities this season and has played just six times in the Premier League under Maurizio Sarri.
However, the Italian has expressed a desire for Fabregas to remain at Stamford Bridge.
Sarri said: “In this position we have only two players, Jorginho and Fabregas, so for me it would be really a problem without Cesc.
“I want him to stay, I don’t know the final decision of Cesc and the club of course.
“But for me it’s very important and if Cesc will go I think that we need to buy another player, and it’s not easy because, technically, Cesc is a very important player.
“And I think that in the market it’s very difficult to find a player with his characteristics.”