The royal couple, who have just returned from the Maldives, were attending the St Patrick's Day parade of the Irish Guards - of which Prince William is the honorary colonel - when the remarks were made in answer to a soldier's question.
The prince's reply quickly appeared on Twitter via royal correspondent Rebecca English.
English said that the prince's remark was made in response to Regimental Sergeant Major Ray Collister's cheeky enquiry asking if there were any 'baby Micks' (slang for an Irish Guardsman) on the way. Laughing, the prince is reported to have answered: "Maybe one day. One's enough at the moment."
Further quashing pregnancy rumours, the duchess was pictured cheerfully joining William to quaff samples of sherry and Guinness as they mingled with the men and officers of the regiment. English reported that the pair freely answered questions about Prince George.
This is the second year the Duchess of Cambridge has joined her husband to present the Guardsmen with fresh shamrocks. She performed the duty alone in 2012 while the Duke was serving in the Falkland Islands. Last year, while pregnant with baby George, she got the heel of her shoe stuck in a grate at the event.
As she has done in years past, the Duchess went all-out with her wardrobe to honour the saint's day, dressing head to toe in green - even down to a subtle shade of emerald eyeshadow.
She set the look off with a gold Cartier shamrock brooch belonging to Queen Alexandra, who presided over the first presentation ceremony in 1901.