But Camilla, the Duchess of Cornwall, revealed publicly Monday that the baby was expected by the "end of the week."
Accordingly, Prince William has a chartered helicopter on standby for an "heir-lift" to the hospital when labor begins.
Camilla and Charles, Kate Middleton's in-laws, hinted at the baby's arrival during their annual summer tour of Cornwall, where they ran into new mother Trudi Lindsay.
"I said, 'You have got one of these coming soon' and Charles replied, 'Hopefully!' Then he laughed," Lindsay said, holding three-month-old daughter Ellie-Mae.
Kensington Palace has not released an official due date, and has said it would not provide any notification as to when Kate goes into labor. When the baby arrives, if a name has been chosen, the palace will display the name in a frame on an easel.
The royal parents have decided not to find out the sex of the baby until he or she arrives. Either way, a recent change in the law of royal succession will allow a child of either sex to become the third-in-line heir to the throne.