The couple decided against an immediate overseas honeymoon after getting married in London on April 29.
Palace officials are remaining tight-lipped about plans, but said the prince did take two weeks leave from military duty as a search-and-rescue helicopter pilot. They also requested the young couple's privacy be respected during that time.
It's rumored the honeymoon is taking place in the Seychelles, which is an archipelago of 115 Indian Ocean islands. A popular luxury destination, it lies outside the cyclone belt, so severe storms are rare, adding to the destination's appeal.
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.
If the couple has 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.
The Associated Press contributed to this story