"He's been joking about becoming a great-great- granddad and still performing!'' the Post quoted a source close to the 70-year-old musician as saying.
Assisi is the daughter of Jagger's 42-year-old daughter Jade. The Rolling Stones front man has seven children with four women.
The Post did not report the gender or anticipated due date of Assisi's first child with her boyfriend, who was not identified.
Celebrity Families of 2014 [PHOTOS]