Luiz' deal runs out in July, however he has been telling sources at the club that he would like an extension.
The Brazilian defender, who was a standout performer in Saturday's 2-0 win over Manchester City, is in the final year of his contract.
"I am just trying to enjoy myself, like I do every single day," Luiz told 'Sky Sports'.
"Then, for sure, we will do the best thing for me, for Chelsea, for everybody."
Asked whether or not he would accept a one-year extension, Luiz replied: "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 gave a timely reminder of his qualities to Chelsea's decision makers on Saturday as he scored a goal and played a large role in holding City scoreless for only the second time this season.
City's lead over Chelsea has now been cut to seven points, while Liverpool are eight ahead, and Luiz hopes the Blues have provided a blueprint to the rest of the league of how to beat Pep Guardiola's side.
"I hope, I hope, I hope so," said Luiz. "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."