"We have suspended all of our markets apart from the name of the baby, where Ivy is currently the short-price favourite on the back of a surge of bets in the last 48 hours," John Hill, Coral's PR Manager, told CNN.
There’s speculation that insiders already know whether Baby Sussex has arrived.
"These people are clearly talking to someone, who is talking to someone else," Lee Price, Paddy Power's head off PR, told CNN.
Ladbrokes suspended betting on where the birth will take place last week.
Closer to home, TAB has placed the name Ivy as frontrunner for Baby Sussex, followed by Diana, Grace and Victoria.
The Duchess, 37, was last seen in public on March 19 at the New Zealand High Commission in London where she paid her respects to the victims of the shooting at two mosques in Christchurch.
With Meghan and Prince Harry, 34, previously stating they want to spend time alone with their new baby before they announce news of the birth to the public, it could be some time before we know any of the details.