Kate, who is on a royal visit to Canada with husband Prince William, was on public walkabout in Quebec when she was presented with a bouquet by Raffaela, the two-year-old daughter of British ex-pat David Cheater.
Mr Cheater then asked Kate if she was planning to have children soon, to which the Duchess of Cambridge replied: “Yes, I hope to.”
It is the first time she has told of her desire to have children.
Kate Middleton is a natural with children and has a Princess Diana-like quality to be at ease with them.
Mr Cheater, 28, who queued in the centre of Quebec for four hours with his daughter to see the royal couple when they visited the City Hall to attend a ceremony honouring the Canada's Royal 22nd Regiment, said: “It's a real honour to meet any member of the royal family for me as I'm a royalist.
“I was hoping but I didn't think it would happen.
“Kate said to me 'what a beautiful daughter you have'.”