According to UK bookmaker William Hill, punters are predicting a girl with Diana reigning with odds of 10/1.
Alice comes in at second place (12/1) followed by Victoria (14/1) and Alexandra (16/1).
However, if the royal newlyweds welcome a son, Arthur is the number one choice (12/1) with Edward (16/1) and James (16/1) following closely behind.
Unsurprisingly, royal baby names are proving profitable with the market up by 80% in comparison to the run-up to Prince George’s birth back in July 2013.
“Royal baby betting has never been more popular and the public clearly love Harry and Meghan,” Rupert Hill, of William Hill, said.
“At this stage we think turnover will be higher for the Sussex baby than it was for Prince George,” he continued. “The killer blow for the bookies is for the baby to be a girl and for them to choose to call her Diana.”
But how likely is it for Prince Harry to name a daughter after his late mother?
It’s interesting to note that the Duke and Duchess of Cambridge’s daughter, Princess Charlotte, was given the middle name, Diana, in memory of the royal.
The three-year-old was also given the second middle moniker, Elizabeth, in tribute to her great grandmother, Queen Elizabeth II.
However, it’s not unusual for members of the Windsor clan to share names.
Prince George was given the middle name, Louis, which is also the name of his younger brother. While Prince Louis was given the middle name, Charles, in honour of his grandfather, Prince Charles.
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So it won’t come as a complete surprise to royal fans if Harry and Meghan decide to pay tribute to Princess Diana.
Competitor Paddy Power is also proof that the name is a real contender as the regal moniker has been the favourite (8/1) since the bookmaker first started taking bets.