David Luiz’s future at Chelsea beyond the summer has been cast into considerable doubt after the club’s hierarchy made it clear they are reluctant to change their policy of offering only one-year contract extensions to players in their 30s.

The club are seeking to prolong the stays of some key personnel, not least because they are one of a number of English sides under investigation by Fifa over possible violations of rules on the signing of foreign players under the age of 18 and could be the subject of lengthy transfer embargoes if found guilty by the world governing body’s disciplinary committee. Marcos Alonso, N’Golo Kanté and César Azpilicueta have all agreed new terms recently, and are likely to be followed in the near future by Antonio Rüdiger.

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Yet David Luiz, like Cesc Fàbregas and Gary Cahill, is entering the final six months of his deal with his situation rather more delicate. The Brazil defender, in his second stint at the London club, was outstanding in Saturday’s victory over Manchester City, scoring the hosts’ second goal and showcasing his best qualities throughout as the champions were beaten in the Premier League for the first time this term. The 31-year-old has reaffirmed his commitment to Chelsea and would ideally like to stay, and Maurizio Sarri indicated last week his preference would be to retain him.

However, David Luiz would want more than the 12-month extension that is currently on the table, aware as he is that he would be able to secure longer terms elsewhere. Foreign clubs can start negotiating with him from January over a summer move under freedom of contract and, with Chelsea having indicated they are unwilling to shift their long-standing stance on players over 30, there remains a strong possibility that the centre-half will depart in the summer under the Bosman ruling.

“I am just trying to enjoy myself, like I do every single day,” said David Luiz when asked about the uncertainty over his future. “Then, for sure, we will do the best thing for me, for Chelsea, for everybody. We are still talking, let’s see. Let’s see what the future brings. I love this club, everybody knows I want to stay.”

Cahill is expected to leave on loan in January before departing permanently on a free transfer in the summer, while Fàbregas, who is now considered Jorginho’s understudy and has started only one Premier League game this season, is attracting interest from clubs in France and Italy.

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Sarri will be reluctant to lose any key players in January and revelled in the defensive excellence of his veterans David Luiz and Azpilicueta, on Saturday. City had not lost in the league since early April but, having dominated the opening half, were punctured by Kanté’s opening goal just before the interval. David Luiz had played his part in that with a glorious cross-field pass from deep to Pedro on the right flank, and would rise to meet Eden Hazard’s corner to confirm the win 12 minutes from time.

Asked if Chelsea’s success may have wounded City, whose start to their title defence had been so imperious, David Luiz said: “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 [who have played] 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.”

Chelsea’s back-line had been made to look rather more vulnerable in their recent loss at Tottenham Hotspur, but both Sarri and David Luiz suggested City’s imposing reputation had helped focus minds to instil a more disciplined defensive display. “The way they play, they are able to keep the ball, even the goalkeeper is amazing,” he added. “You have to be honest and have the humility to say: ‘OK, we have to defend, we have to suffer because we play against a fantastic team.’ They create many opportunities if you don’t concentrate.”

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Sarri had dropped Álvaro Morata from his match-day squad, preferring to use Hazard as a false No 9 with Olivier Giroud as an alternative on the bench, but offered the Spain forward hope he will be involved in Sunday’s trip to Brighton. Morata was at Stamford Bridge and undertook a warm-down session on the pitch after the final whistle. “I don’t know if in Brighton we will play in the same way or not, maybe not,” said Sarri. “But Álvaro is able to understand that it is only a tactical decision, not the final choice.”