Closer magazine in France claims to have world exclusive, long-lens photographs of the couple on a recent private break in Provence, and trailed the images on its website ahead of planned print publication later today (Friday, September 14).
It has released a pixellated version of the cover which appears to show three images - two of a man and woman and one of a woman adjusting her bikini top - with the headline "Oh my God! Les photos qui vont faire le tour de monde!" ("Photos that will be broadcast around the world").
Sky News has reported that although it is yet to be established if the photos are genuine, St James's Palace is consulting French lawyers.
A spokesperson said that William and Kate feel "very angered" and believe that "a red line has been crossed" by the magazine.
A senior palace source told the Daily Mail: "The Duke and the Duchess were told at breakfast and are obviously saddened and disappointed if they are genuine as they believe they have a right to privacy - particularly on holiday. This incident turns the clock back 15 years."
A second insider added: "It is impossible to tell at this stage whether the photographs are genuine or indeed purport to show what the magazine claims, so we are having to wait and see what transpires."
The couple are currently in Kuala Lumpur on an official tour to mark the Queen's Diamond Jubilee.
Photo gallery - A year of the Duchess of Cambridge:
Copyright: PA Images