David Luiz is keen to stay at Chelsea but wants more than the one-year contract extension that he has been offered.
Chelsea remain hopeful that Luiz's central defensive partner Antonio Rudiger will sign a new deal at Stamford Bridge.
N'Golo Kante, Marcos Alonso and Cesar Azpilicueta have all signed new contracts at Chelsea this term.
Luiz is entering the final six months of his current contract, and has insisted he wants to stay at the Blues.
The Brazilian centre-back has been offered a new one-year contract at Chelsea; but the 31-year-old wants a longer deal as he approaches the second half of his footballing career.
"I am just trying to enjoy myself, like I do every single day," Luiz said to Telegraph Sport. "Then, for sure, we will do the best thing for me, for Chelsea, for everybody."
Asked whether he would accept a new one-year deal, Luiz answered: "We are still talking, let's see. Let's see what the future brings.
"I love this club, everybody knows I want to stay."
Luiz scored in Chelsea's 2-0 win over Manchester City on Saturday evening, with Chelsea inflicting the champions' first defeat of the season.
The defender was asked whether Saturday's defeat would open up a wound in the City team, and replied: "I hope, I hope, I hope so.
"But I also know they are a fantastic team and they accept to lose sometimes too because they have experience of that. But I hope we hurt them and we can move up the table and be closer to them.
"At the moment, they are the best team in the world; more than three years together. It is never easy to play against them, but I think we had the right humility and right plan to win the game.
"When you play this type of game, it is a time to give everything and understand how far you can go. So this was an amazing game and we beat the best team in the world."