Kate, however, looked to dampen the speculation by drinking wine and going on a jet boat ride, neither of which are recommended for pregnant women.
The royals' eight-month-old son Prince George, third in line to the British throne, has been the star of their New Zealand tour so far.
But William suggested during a walkabout in the North Island town of Cambridge there may soon be another royal baby to share the spotlight.
During a meeting with Cynthia Read, who knitted the merino wool shawl which was New Zealand's official gift when George was born, William said according to several reports: "You might have to make another one soon!"
Read, who emigrated to New Zealand from England eight years ago, was convinced the prince was serious.
"The way William said it was like he was dropping a hint, letting me in on a secret," she told reporters, adding the duchess said they were delighted with the first shawl "and George wore it a lot".
Kate was also seen to be sipping water during an evening state reception for the couple on Thursday, fuelling media speculation of a second pregnancy.
During a visit to a vineyard in the acclaimed wine-producing area of Queenstown today there was intense interest in whether Kate would indulge in a drop or two.
Central Otago Pinot Noir Ltd chairwoman Lucie Lawrence, who escorted the duchess at Amisfield Winery, said she had "six or seven" tastes.
"She was drinking it. She really enjoyed drinking the Pinot Noir," Lawrence said.
William did not hold back and after a brief tour of the winery he remarked to co-owner John Darby: "We should probably stop the talking and start the drinking".
There was also no keeping Kate from accompanying William on a wild jetboat ride on the Shotover River, racing through shallow water at speeds of up to 85 kilometres per hour (53mph).
The couple flew to Queenstown from the southern city of Dunedin where they attended a Palm Sunday service at St Paul's Anglican Cathedral and a junior rugby match with All Blacks captain Richie McCaw.
William, who lost to his wife in a yacht race on Auckland harbour on Friday, exacted a measure of revenge on the rugby field when the team of eight-year-olds he helped coach beat Kate's side 30-20.