Christensen’s contract in West London will be due after the conclusion of the 2021/2022 season, but the 25-year-old has revealed that both him and the club are making progress in their discussion for a new deal.
The former Borussia Monchengladbach loanee has found a new life in London since the arrival of head coach Thomas Tuchel.
Christensen has played 23 times for Chelsea since the German tactician was drafted in to replace Frank Lampard and has started all three games so far in the Premier League.
The defender, who is on World Cup qualifying duty with his country, told Ekstra Bladet: "I know a lot is being said right now. I cannot say too much, but I think it looks good.
"We have won the Champions League and the Super Cup. I am very happy to be at this club and feel Chelsea are the right place to be in England."
He added, having overcome a testing period in his Blues career when he fell down the pecking order: "I know Thomas Tuchel believes in me. I have also played a big role since he came.
"I had a very difficult period under [Frank] Lampard, shortly before he was fired. Now luckily it’s going the right way for me. Things can go fast in this world. The most important thing is just that I have never given up."