The 70-year-old Rolling Stones frontman and his family will welcome the new addition when Jade Jagger's daughter, Assisi Jackson, 21, gives birth, The Mirror reported Sunday.
Jade Jagger told the Sunday Times she thinks her father is unfazed by the new title.
"I think making Mick a grandfather obviously had a big impact, whereas, now making him a great grandfather is no longer particularly fascinating," she said.
This will be the first child for Jackson, who is dating a chef identified only as Alex, The Mirror said.
Mick Jagger has seven children aged between 14 and 42 with four different women. His eldest daughter, Karis, was born in 1970 after a fling with Marsha Hunt. Jade Jagger is his only child with Bianca Jagger. He has four children -- Elizabeth, James, Georgia May and Gabriel -- with Jerry Hall, and son Lucas with Luciana Gimenez.
The rocker has four grandchildren, including Assisi and Amba Jackson, and Karis' two children.