Alice was originally tipped as the top girls name, but Ladbrokes now has Mary in the lead, with odds of 7-1.
Mary is one of the Queen's middle names, and it was also her grandmother's name - Queen Mary - who was married to George V.
Currently, Britain has had two Marys on the throne - Mary I, or 'Bloody Mary' as she was more commonly known, and Mary II, who ruled jointly as monarch with her Dutch husband, William III.
'We can't quite put our finger on the link between Mary and the North West, but the overwhelming support means we have a new favourite in the royal baby name market,' Jessica Bridge, an employee at Ladbrokes, said.
She added: 'Punters are convinced the Duke and Duchess are expecting another little girl, and obviously it would be a lovely touch to honour Her Majesty's grandmother, but it will be interesting to see if any boys' names are backed over the coming weeks before the birth.'
Ladbrokes has Mary at odds of 7-1, followed by Alice and Victoria at 8-1 and Alexandra at 16-1, while Albert or Arthur are 12-1 for a baby boy.