The odds on gender, however, are even, according to William Hill.
However, on Sportsbet.com.au, royal watchers think there is a slim chance the child is more likely to be a boy than a girl, with bets on the sex starting at a short $1.90 for a boy and $2 for a girl.
According to The Sun , however, traditionally royal parents don't find out the sex of their child until it's born. The new site, however, notes that Princess Diana reportedly knew she was having boys.
Betting website, William Hill, have Mary (3/1) and Alice (6/1) listed as the top two most likely girls names, as early frontrunners Elizabeth (12/1) and Victoria (8/1) have fallen down the list.
Mary is a popular name with the royals — it is Queen Elizabeth's middle name and was also the name of her grandmother.
Another popular UK bookmaker, Coral, has Alice and Mary both at 5/1 and Victoria at 8/1 - as does Ladbrokes.
Coral's John Hill told Expressthat interest in the royal baby name betting is really hotting up as Kate's due date grows closers. "At the moment, many punters are convinced it is going to be a girl and it will named Mary," he said
There's also been some suggestion that if the baby is a girl, she may be named after Prince William's mother, the late Princess Diana. William Hill has the odds at 20/1.
If the baby is a boy, the top names are currently Albert, Arthur, Fred or Frederick are all leading the charge at 12/1.
Coral also has Albert and Arthur at 12/1.
"The girls' names have been dominant at the head of the betting leading to speculation that people might know that a girl is on the way however with the due date surely just a matter of weeks away, the boys' names are starting to attract a bit of cash," said William Hill spokesman Joe Crilly. "I imagine that Kate would push back on baby number three being named after a footballer though."
Putters are also betting on the names James, Alexandria, Grace, Phillip, Alexander, Henry, Olivia and Catherine.
Other, far less traditional, names have also been suggested, including Donald, Chardonnay, Olympia and Tyrone — all with odds of 500/1.
As for the date of birth, most punters on Sportsbet.com.au are hedging their bets the baby will arrive this week, with bets starting at a short $2.50. The week starting April 23 is the next best bet at $2.80, however, for those who think the baby may be late, bets on her giving birth from April 30 start at a long $5.50.
