Despite the claims, the couple previously said shortly after getting engaged, they were in no rush.
"I think we'll take one step at a time," Prince William said at the time.
“We'll sort of get over the marriage first and then maybe look at kids, but obviously we want a family so we'll have to start thinking about that.”
Yet royal correspondent Robert Jobson says that having children “one of the prerequisites of the job as an heir to the throne".
“In truth, his [William’s] number-one priority, securing the line of succession, is one of the prerequisites of the job as an heir to the throne," the author claimed in his book “William and Kate: The Love Story”.
And shortly after getting married Kate and William welcomed their first child in 2013, followed by their second child in 2015 and their third child in 2018.
The news comes after rumours that Kate is expecting her fourth child.
"A baby girl is on the way of the radiant royal couple,” a royal insider told Star magazine.
Kensington Palace is yet to receive an official statement on the claims.