The £23million signing from Fiorentina has been linked with a switch back to Real Madrid, where he started his career.
Alonso told AS: “I never saw myself outside Chelsea this summer. I am very happy there, I have three years left on my contract and my idea has always been to stay.
“In England I feel very well known, not only by Chelsea fans, but also other teams.”
Alonso has scored 15 times for the Blues since joining the club in 2016.