UsMagazine.com and E! News said the British royal couple were accompanied Friday by their security detail back to the city where Kate is expected to give birth to their first child.
UsMagazine.com said it was unclear whether they were heading to St. Mary's Hospital or to their home at Kensington Palace.
"We wouldn't comment on the exact whereabouts of the duke and duchess -- we wouldn't normally do so in their private time," a palace representative told the celebrity news magazine about the labor speculation.
The baby's expected due date has not been revealed, but it is widely believed to have passed this week.
The gender of the future prince or princess of Cambridge will not be known until he or she is born. The baby's parents' titles are the duke and duchess of Cambridge.
William and the former Kate Middleton -- who are both now 31 -- married in April 2011.