British media widely reported they had jetted off to the Seychelles, an island chain in the Indian Ocean. William has two weeks leave from his job as a search-and-rescue helicopter pilot, but palace officials would not say if they will be away the entire two weeks.
After the media blitz surrounding their April 29 wedding at Westminster Abbey, the couple have made it clear they'd like to be left alone by photographers. A day after the wedding, the newlyweds asked the media not to intrude on their first weekend of married life, which they spent at home before William returned to military duty.
Privacy has long been a main concern for the royals while planning their honeymoon. They are thought to have considered private islands in the Caribbean — although photographers on boats could conceivably get pictures of them cavorting on a beach — and hideaways in Africa, where William has traveled extensively in the past.
The couple's decision earlier to delay their honeymoon surprised many. While he went back to work, Middleton — now known as the Duchess of Cambridge — was snapped by photographers grocery shopping near the couple's home on the remote Welsh island of Angelsey.
The Seychelles is an archipelago of 115 Indian Ocean islands about 1,000 miles (1,600 kilometers) east of the Kenyan coast. A popular luxury destination, it lies outside the cyclone belt, so severe storms are rare, adding to the destination's appeal.
Srdjana Janosevic, the press secretary for the Seychelles' president, had no confirmation Tuesday that the royal couple had arrived or planned to vacation there, but noted they have visited the Seychelles before.
"Anyone who comes back and continues to enjoy the island, it just shows that it's a very desirable tourist destination," Janosevic said. "I think everyone would be happy if they are here."
The Seychelles has only about 90,000 people. While the British media feature constant stories on the royals, a top headline Tuesday in the Seychelles Nation newspaper was about an increase in pork and chicken production.
The top local topic is the country's May 19-21 presidential election, where President James Michel faces three challengers.
If the couple have chosen the Seychelles, it will be East Africa's second connection to the royal wedding. William proposed to Kate last October in a rustic log cabin on the slopes of Kenya's highest peak, Mount Kenya.
Both Kenya and the Seychelles are former British colonies.