While the due date is a closely-guarded secret, Meghan, 37, told well-wishers in Merseyside that the baby is expected to arrive at the end of April or beginning of May.
If the little one arrives within that period of time, he or she could end up sharing a birthday with some other members of the Royal Family.
The Queen turns 93 on April 21 and Meghan and Harry’s child will be her eighth great-grandchild.
She’s already a great-grandmother to Savannah, eight, and Isla Phillips, six, Peter Phillips’ children with wife Autumn. Prince George, five, comes next, followed by Zara and Mike Tindall’s firstborn Mia Tindall, who’s also five.
Princess Charlotte, three, is the fifth youngest, followed by younger brother Prince Louis, who turns one this month. Zara and Mike’s second child, Lena, is the current youngest of the group at just nine-months-old.
If Meghan and Harry’s baby arrives on April 23, they will share a birthday with cousin Prince Louis, who is set to turn one.
The Duke and Duchess of Cambridge have kept their youngest child out of the spotlight since his birth last year, but royal fans are hoping the couple will release an official photo to mark the occasion.
If Meghan goes into labour in May, her baby could share a birthday with Kate and William’s second child Princess Charlotte.
Their only daughter will celebrate her fourth birthday on May 2 and will reportedly join her older brother George, five, at Thomas’s Battersea school in September. Charlotte currently attends Willcocks Nursery School in Kensington.
Mum-to-be Meghan currently has no more public engagements scheduled until the birth. She and Harry are expected to move to their new home Frogmore Cottage in Windsor, before the baby arrives.
The duke and duchess have just launched their own Instagram account, where they will share the work they do, the causes they support and important announcements. Looks like it’s been set up just in time for the arrival of Baby Sussex.