The Spaniard is out of contract in the summer and was asked whether he would be interested in signing an extension, per Vaishali Bhardwaj at the Evening Standard:
"Yeah I'm very open about it.
"To be...honest the club has not said anything. At the end of the day I have eight months left and at the moment I'm gone. But I'd love to stay at the club.
"I've been very happy for the last four years and a half, we've had great success, won many things. I think I have a good understanding with the fans and players. I feel I still have a lot of football left in me but it is now up to the club."
Fabregas has yet to feature in the Premier League under new manager Maurizio Sarri, although he was sidelined in the early weeks with a knee injury.
In his absence Jorginho, N'Golo Kante and Mateo Kovacic have emerged as Sarri's preferred midfielders, and the Blues have started the season well. They have yet to taste defeat in the Premier League after seven games.
Fabregas did feature in Chelsea's UEFA Europa League win over Hungarian side Vidi on Thursday. WhoScored.com highlighted his contribution:
If he can stay fit, Fabregas has plenty to offer Chelsea and could prove an important squad player. He is intelligent and experienced and has already won two Premier League titles, the FA Cup and the EFL Cup with the Blues.
Sarri has said the midfielder can be a "great option" for Chelsea as a back-up to Jorginho:
Yet the 31-year-old does not expect to see out his career at Chelsea, per Bhardwaj.
"I don't think so," he said. "Probably in a few years, I'd like to go away from Europe and experience something different at the later stage of my career. But for now, I still feel really good."
Fabregas may no longer be first choice at Chelsea, but it would still make sense for the Blues to offer him a short-term extension rather than see him walk away for free in the summer.
The midfielder appears keen to stay but looks to still have work to do to convince the club he is worth a new deal.