The Spain international was said to have been angling for a move away during the summer after being used 16 times from the bench in the Premier League last season.
Fabregas has already featured 11 times under Antonio Conte in all competitions this term, however, and the 30-year-old is more than happy to stick around in West London after adding a couple of top-flight crowns to his collection since joining.
"I have found absolute happiness at Chelsea," he told Vanity Fair. "My family is delighted, they have totally adapted to life in London – I'm too happy to change clubs. I just miss my family and my friends in Barcelona.
"You can get distracted by fame and money or the wrong type of people. I have seen young people with tremendous talent fail. And, to the contrary, I've seen less gifted players triumph on the basis of their attitude and commitment. Have a good head. Being surrounded by people who really love you is very important."
Fabregas, who grew up in London playing for Arsenal, has featured more than 100 times for Chelsea in the league since arriving from Barcelona in 2014.