The wait for the birth of the prince or princess continues and Kate - who said her baby was due in mid to late April - is now several days overdue.
Charles' confession came when he met Welsh Guardsmen, veterans and their families after the Queen presented new colours to the 1st Battalion Welsh Guards at Windsor Castle.
At a reception the heir to the throne chatted to 100-year-old Eric Jones, the oldest surviving member of the Welsh Guards, who made Charles laugh when he joked about having daughters.
The centenarian's daughter Lynda Bateman said: "My father introduced me as his daughter and Prince Charles asked how many daughters he had.
''My father said 'One - and that's enough' and Charles laughed and said 'And we're hoping for a granddaughter!'''
The arrival of the royal baby - who will be fourth in line to the throne - is edging closer to the bank holiday weekend and the General Election on May 7, which is just one week away.
The Duchess of Cornwall told the wife of another veteran that there was still no news about whether Kate was about to go into labour.
Maureen Morris, whose husband Bill served with the Welsh Guards between 1952 and 1955, said: "I asked if she had any news and she said; 'No'. I said; 'It will be great when it happens'."
Avid royalists have been waiting along with the world's media outside the Lindo Wing, the private maternity unit of St Mary's Hospital in London, for any news of the duchess going into labour.
But one avid monarchy fan was left feeling "over the moon" after receiving an 80th birthday cake from the Duke and Duchess of Cambridge.
Terry Hutt, who is camped outside St Mary's, said he was "overwhelmed" to be recognised by the royal couple.
The cake, thought to be a chocolate treat, was delivered in a box wrapped in pink and pale green ribbons and came with a handwritten card that had the Duke's cypher.
It said: "This comes with our best wishes on your 80th birthday from the team at Kensington Palace."
Mr Hutt, 80, from Weston-super-Mare has been waiting patiently outside the hospital for 10 days and joked about being recognised by the royal couple, saying "I know they like me anyway".
Asked to read the message on the card he said: "I can't see without my glasses, I think it's something nice", adding he would keep it in cabinet along with his trophies and special invitations.
Well-wishers have been giving the 80-year-old cakes throughout the day but he said his Kensington Palace gift would be saved: "I'm going to wait for tomorrow for this one."