She added: “But on the other hand he does bring it up, meaning it could be on his mind too.
“The slightly suppressed grin hints that he could possibly be persuaded to add to their family if Kate did happen to put the pressure on gently.”
William and Kate have three children: Prince George, eight, Princess Charlotte, six, and Prince Louis, three.
For the engagements in Lancashire, Kate wore an all-camel outfit consisting of a long wool coat, a knitted turtleneck and a matching skirt, and knee-high boots.