According to Kieran Gill of the MailOnline, though Blues boss Maurizio Sarri wants to see each player remain at Stamford Bridge beyond the end of the season, the club's policy of only offering one-year deals to players over the age of 30 is proving to be a stumbling block.
Gill added that Chelsea have been in talks with both players over extensions, and Sarri said he remains hopeful the club can agree something:
"The deal is very difficult for this reason, I think. Because the club wants a short contract, and the players want a long contract. So it's difficult for this reason.
"But I think, at the end, we can find a solution. I know very well that it is not easy but I think that we can do a new deal for both. They are very important players for us. It's very difficult to find a centre back for this level, and it's very difficult to find a central midfielder technically like Fabregas. And so I think they have to stay with us."
The deals of both players are set to run out at the end of the campaign, meaning, starting in January, they could each discuss terms with teams from overseas over signing a pre-contract with a view to a summer move.
So far this season Luiz has been a key man for Sarri, re-establishing himself as the Blues' leader in defence and playing every minute of every Premier League game so far this term, forming a strong partnership with Antonio Rudiger.
However, the Brazil international has always been prone to mistakes in games and made a few peculiar decisions in the 3-1 loss to Tottenham Hotspur recently:
Fabregas has been more of a peripheral figure this term and has yet to start a Premier League game under Sarri. However, in the Carabao Cup and the UEFA Europa League, he's shown he still has something to offer and has been a fine alternative to Jorginho at the heart of midfield.
Of the two players, it's Fabregas whose future seems to be most in doubt, as it's been reported by Corriere dello Sport (h/t Sport Witness) that AC Milan are ready to intensify their efforts to sign him in January.
Per Italian football journalist David Amoyal, key figures at Milan have spoken about a possible switch too:
In addition to the two players aforementioned, the likes of Olivier Giroud and Gary Cahill also have contracts due to run out at the end of the season, meaning the Blues may be in for a busy stint of negotiations.
While it appears there's a desire to keep both Fabregas and Luiz at Stamford Bridge, it would be understandable if either player opted for a switch elsewhere, as a long-term deal would clearly be more favourable as they each enter the twilight years of their career.