Diana, which is of course the name of Harry's late mother, trails closely behind on $6, while Allegra and Elizabeth are tied third at $11.
"The support for baby Philippa is showing no signs of slowing down, and we've been forced to trim the odds again that it's the name for Harry and Meghan's daughter," Jessica O'Reilly of Ladbrokes told People.
Meghan and Harry surprised bookies when they named their son Archie, with the popular suggestions at the time being Arthur, Charles and Albert.
Harry's cousin Princess Eugenie also honoured Philip in her first child's name, after giving birth in February with husband Jack Brooksbank.
The couple named their new son August Philip Hawke Brooksbank.
Meghan, 39, and Harry, 36, told Oprah Winfrey in their bombshell interview in March they were expecting a little girl after announcing their pregnancy on Valentine's Day.
"To have a boy and then a girl, what more can you ask for? But now we've got our family. We've got the four of us and our two dogs," said Harry, after revealing the couple's forthcoming second child is a girl.
Harry earlier told the September issue of British Vogue – which Meghan guest-edited – that he wanted "two (children) maximum".