Gaga, 26, is also said to be keen to strike up a friendship with Pippa.
The source added: "By reading the book Gaga hopes it will give them something to talk about should they ever meet up.
"She would love to get pally with Pippa. She's been intrigued by her since the royal wedding."
Gaga has made no secret of her affections for the royal family, previously saying the late Princess Diana was one of the "most important" people in her life growing up, and writing a song in tribute to her, Princess Die.
Meanwhile, Pippa, 29, has been spotted dating two hunky bankers in the space of a week. She stepped out with Tom Kingston on Thursday, visiting private members club LouLou, days after she was spotted dining with James Matthews, a chief executive of Eden Rock Capital Management Group.
Pippa has been single since splitting from long-term boyfriend Alex Loudon last year.
- BANG! Showbiz