Although the gender of the baby has not been confirmed, Ladbrokes have recently boosted the odds for the name Mary to be the moniker of choice for the royal couple's third child.
The odds for the baby being named Mary are now at 7/1, previously stood at 20/1.
Other bookies have even suspended betting on whether the child will be a girl or boy.
Alice, which was previously the number one pick, has fallen to 8/1, in second place with Victoria.
Names Albert and Arthur are the favourite's for a boy, with odds of 12/1.
Mary's rise to top spot came after a surge of betting on the name from the North West of England.
"We can’t quite put our finger on the link between Mary and the North West, but the overwhelming support means we have a new favourite in the royal baby name market," a Ladbrokes representative said.
"Punters are convinced the Duke and Duchess are expecting another little girl, and obviously it would be a lovely touch to honour Her Majesty’s Grandmother, but it will be interesting to see if any boys’ names are backed over the coming weeks before the birth."