Jane met with Prince Harry and Meghan Markle for a conservation conference at St George's House on the grounds of Windsor Castle, in June.
Of their meeting, Dr Jane Goodall said: "Harry asked if I would go and meet him. They made me a dame of the British empire so I guess he thought it would be good to meet me. And we clicked."
Jane then revealed that she got to cuddle Archie, saying that he is "very cute and very gentle."
Archie Harrison was recently christened in a private ceremony in Windsor, and the identity of his godparents are being kept private.
Archie's most recent public appearance was at a charity polo also attended by the Duke and Duchess of Cambridge and their three children, Prince George, Princess Charlotte and Prince Louis.