Mary, 38, who already has two children, eight-year-old Arthur and five-year-old Elliot, with ex-husband Alistair Donald, is expecting her first child with her filmmaker partner Simon Aboud.
A source said: "They don't know whether it's a boy or a girl and they don't want to."
"Everyone is delighted and they are very happy."
Photographer Mary, whose mother was Paul's late first wife Linda, and former advertising creative director Simon started dating last year after bonding over a mutual passion for the arts.
The source added to Britain's Daily Mail newspaper: "Like Mary, Simon loves photography."
"They don't like a lot of fuss and they often go out separately so as not to draw attention to themselves."
The couple's baby will be the former Beatle's sixth grandchild. Mary's sister Stella also has three children, three-year-old Miller, 15-month-old Bailey and two-month-old Beckett, with publisher husband Alasdhair Willis.
Mary and her first husband Alistair, who married in 1998, the year Linda lost her battle with breast cancer, officially separated in April 2005 and divorced two years later.
