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The Queen, who turned 92 on the weekend, will be the first person to be told of the birth of the baby, who will be fifth in line to the throne.
The boy or girl will be the Queen's sixth great-grandchild and its arrival will relegate Prince Harry further down the line of succession to sixth.
Uncle Harry and aunt-to-be Meghan Markle will be on hand to dote on the royal baby when the prince or princess arrives.
The couple are neighbours of the Duke and Duchess of Cambridge at Kensington Palace, living in Nottingham Cottage in the grounds of the royal residence.
Markle, the former US actress, recently hinted at having her own children with Prince Harry.
On a trip to Belfast, she joked that when she was shown an innovative range for newborns: "I'm sure at some point we'll need the whole (lot)."
Barriers were erected on April 9 outside the Lindo Wing of St Mary's Hospital in preparation for the royal baby.
Photo: APIn an interview in 2016, Markle said becoming a mother was on her "bucket list".
"I can't wait to start a family, but in due time," she said.
Prince Harry has also said he would love to have children.
The topic cropped up in the couple's engagement interview.
"You know, I think one step at a time, and hopefully we'll start a family in the near future," the prince said.
Kate, the Duchess of Cambridge, on St Patrick's Day this year in Hounslow, England.
Photo: APMarkle has been spending time getting to know William and Kate's eldest children, Prince George and Princess Charlotte.
The celebrity, who shot to fame playing paralegal Rachel Zane in the American drama Suits, already has two "fairy god-daughters".
She described the children of her close friend Benita Litt as such in a 2016 post on her since-deleted Instagram account.
The bride-to-be and Prince Harry, who will wed in Windsor on May 19, will be among close family expected to attend the christening of William and Kate's baby in a few months time.
with AAP and wires
Latika Bourke is a reporter for The Sydney Morning Herald and The Age based in London. She has previously worked for Fairfax Media, the ABC and 2UE in Canberra. Latika won the Walkley Award for Young Australian Journalist of the Year in 2010.
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