Closer says the pictures were taken when the duke and duchess were on holiday last week at the French chateau of the Queen’s nephew, Lord Linley.
The photos are blurry and taken with a long lens but are clearly of the royal couple, who are touring the Far East, the BBC’s Paris bureau says.
They were told about the magazine’s plan to publish the photos during breakfast in Kuala Lumpur, Malaysia.
It has emerged that British newspapers were offered photographs last week but turned them down.
Officials said the couple were “saddened and disappointed” about what they considered to be a breach of their privacy.
The publication of the photographs will be a bitter blow to the Duke and Duchess of Cambridge.
Prince William witnessed the complex relationship his mother, Diana, had with the media. He believes the actions of the paparazzi in Paris contributed to her death.
He wants to shield his wife from the worst excesses of reporters and photographers in full flight.
The royals – who only last month suffered the embarrassment of pictures of a naked Prince Harry being widely disseminated – will have to decide what, if any action to take.
Could they pursue the magazine or the photographer through the French courts?
As things stand, they may well decide to do nothing and leave it to the public to pass judgement on the mindset of an individual who takes pictures of a woman sunbathing topless on a private property.
It’s how some photographers have always behaved. It’s how some British papers once behaved. The royals will be hoping history is not about to repeat itself.
An internet trailer for the magazine claims to show Kate in a pixilated picture apparently removing her bikini top while at the chateau in Provence.
The royal couple continued with their nine-day tour, which is part of the Queen’s Diamond Jubilee celebrations, on Friday by visiting a mosque in Kuala Lumpur.
On Thursday, the duchess gave her first official speech abroad while visiting a hospice in the capital.
“Providing children and their families with a place of support, care and enhancement at a time of great need is simply life changing,” she said.
She said the couple were “hugely excited” to be in Malaysia, after they had started their tour in Singapore.
The claims about the magazine photos follow controversy over the publication of pictures of a naked Prince Harry, Kate’s brother-in-law, which were taken in a Las Vegas hotel room last month.
The images first emerged on entertainment gossip website TMZ in the US before going global.
However, the Sun was the only British newspaper to defy the wishes of St James’s Palace and print them after the palace had warned that the photos breached Harry’s privacy.
The tabloid printed two photographs, believed to have been taken on a camera phone, of the prince with a naked woman. It argued that its action were in the public interest.
The Press Complaints Commission said it received hundreds of complaints from members of the public but did not act because it had not been contacted by representatives of the prince.