A punter has placed a £500 wager with William Hill on the duke and duchess having a baby girl in the coming weeks.
“It was just the one bet but it is over one hundred times the average wager on this market,” said William Hill spokesman Rupert Adams.
He added: “We have not changed the odds but will be keeping an eye on the market.”
The bookmaker has made the name Diana its favourite with odds of 10/1, followed by Alice 12/1 and Victoria 14/1.
Meghan gave a hint about her due date when she visited Birkenhead with husband Harry on Monday, confirming she was six months pregnant and saying her baby was expected at the end of April or beginning of May.
Alex Apati from Ladbrokes said: “Meghan’s latest comments have forced us into action and, while we’re convinced it’ll be an early April baby, there’s every chance the latest royal will share a birthday with his great nan.”
The Queen’s birthday is on April 21 while the Duke and Duchess of Cambridge’s son, Prince Louis, was born on April 23 and Ladbrokes have given both dates odds of 14/1.