The 27-year-old has been used in every minute of the Blues' eight Premier League games this term, while also featuring in the Community Shield and Europa League.
Alonso, who has been directly involved in three league goals since Maurizio Sarri arrived, is due to be out of contract at Stamford Bridge in 2021.
Despite still having more than two years to run on his existing terms, the Spain international has been offered an extension and appears to be close to putting pen to paper.
"I am very calm and very happy at Chelsea, and the club must also be happy with me because, although I still have two years left on my contract, they have offered me an extension," he told reporters.
"We are talking about it and the talks to renew are already advanced. If everything goes well, I think I will renew before the end of this month - in the coming days.
"My father takes care of that as he is the one who leads the negotiations," he added. "I am 27 years old, I still have two more years and I am going to extend my contract."
Alonso was touted as a target for Real Madrid in the summer, eight years after leaving the Bernabeu.