The singer's daughter Jade told The Sunday Times that her daughter, Assisi, expects to give birth in several months.
Assisi, 21, tells Hello! magazine that Jagger was pleased when she told him the news.
She says, "I imagine it's nice to be a great-granddad, although I'm not sure he likes the idea of getting old, or being called one. I call him Mick - I wouldn't start calling him grandpa."
The Associated Press contributed to this report.
