Ladbrokes said they received a recent flurry of bets following Mr Waley-Cohen's high-profile win on Radjhani Express on Friday in Aintree's Crabbies Topham Chase, prompting their odds to tumble from 66/1 to 20/1.
Mr Waley-Cohen, an amateur rider, was once dubbed 'The Royal Matchmaker' after helping William and Kate rekindle their romance during their brief split in 2007.
Bookies believe someone close to the Royals with inside knowledge may be having a flutter and placing bets on Sam – an abbreviation of both Samuel and Samantha - causing the odds to drop. David Williams, from Ladbrokes, said: "With Sam Waley-Cohen's close links to the Royals it seems punters are putting two and two together and coming up with Sam as their answer for the baby's name."
Simon Clare, from bookies Coral, confirmed they too have had to reduce their odds on Sam in recent days.
He explained: "We have slashed his odds from 66/1 to 40/1.
"Given how close the Duchess of Cambridge is to Sam Waley-Cohen we are also seeing money for Sam or Samuel at 150/1 and Samantha at 200/1 to be their second baby's name."
Mr Waley-Cohen rode Oscar Time to 15th in Saturday's Grand National.
In 2011 the Cambridges invited Mr Waley-Cohen to their Westminster Abbey wedding.
And in 2012 Mr Waley-Cohen - whose relatives include Shell Oil founder, the 3rd Viscount Bearsted - made Kate guest of honour at his marriage to party-organiser Bella Ballin.
According to one unconfirmed report, the Duchess has been told her due date is April 25.
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