Although the official announcement told of a "baby" rather than babies, reports in the US say a recent scan confirmed the double arrival.
William and Kate have kept mum of the sex of their baby
French magazine Point de Vue will run the story on their front cover this week, and bookies have cancelled all bets on the British royals welcoming twins, following a People report which stated that a "significant gamble" had been made in York.
Twins would be welcome news for William and Kate, who have been vocal about their desire to have a large family.
Kate reportedly told friends that she is planning for a big family, with the 32-year-old royal admitting she wanted "at least" three children, according to The Telegraph.
William and Kate with Prince George in Australia earlier in 2014
Kate, who announced in September that she is pregnant again, herself has two younger siblings Pippa, 31, and James, 27. It is thought that the Duchess wants to give her firstborn Prince George and the new arrival – or arrivals – the same sort of family environment in which she grew up.
William has long expressed his desire for a baby daughter, with Kate confirming in 2013 before the birth of George that "William would like a girl." No announcement of the sex of the new baby – or babies – is expected, however.
If the reports are proven true, Kate's babies would be the first twins born in to the British monarchy in six centuries.
Princess Charlene of Monaco is also expecting twins
In 1430, King James I of Scotland’s wife Queen Joan gave birth to two boys – Alexander and James. Alexander was named as the heir to the throne, however in the same year that they were born, Alexander passed away and James became heir.
At the age of six, James's father was assassinated and he rose to the Scottish throne as King James II of Scotland.
Double baby joy would mean the Duchess would follow in the footsteps of Princess Charlene of Monaco, who announced in October that she was expecting twins with her husband Prince Albert, and Crown Princess Mary of Denmark, who has three-year-old fraternal twins Prince Vincent and Princess Josephine.
Crown Princess Mary of Denmark welcomed twins in 2011
William and Kate's second baby is due to arrive in April 2015, Clarence House confirmed in October. Aides said that the pregnant royal is still suffering from Hyperemisis Gravidarum, a severe form of morning sickness but is feeling better.
Kate remained out of the public eyes for some time, but made a stylish return to duty last week with three events.