Speaking to the baking expert, Kate said: "One of Louis' first words was 'Mary', because right at his height are all my cooking books in the kitchen bookshelf.
"And children are really fascinated by faces, and your faces are all over your cooking books and he would say 'That's Mary Berry' ... so he would definitely recognise you if he saw you today."
Louis, who is the youngest child of the Duke and Duchess of Cambridge, made his first appearance with the royal family on Buckingham Palace's balcony to celebrate the Queen's official birthday at the Trooping the Colour in June this year.
The little prince was joined by his parents, Prince William and Kate, and his siblings, Prince George, 6, and Princess Charlotte, 4.
While speaking about the TV special with Mail on Sunday's You Magazine, Mary shared: “It was just lovely observing [Will and Kate] for those three days. When they are together, he’s constantly touching her arm and looking over at her smiling and she’s the same with him. It was very sweet to see because it was so natural."