According to the paper, Gates's luggage was driven to the Storfjord Hotel, 30km outside the city, after he arrived by helicopter yesterday evening.
The Microsoft founder's secret Norwegian holiday first came to light yesterday morning when he took a bobsleigh ride at Lillehammer Olympic Park. He was later photographed with Crown Prince Haakon and his wife Mette-Marit taking a boat trip near Kristianstad.
Brown, a British cinematographer known for his work on Bond film The Man with the Golden Gun, would not confirm that Gates was a guest.
"I can't say either way I'm afraid, not until someone gets him to verify it," he told The Local.
Brown worked on Empire of the Sun before moving into TV commercials. He built the Storfjord Hotel from scratch after falling in love with a run-down old barn he found with his Norwegian wife Annbjørn on a visit from London in 2004.
The couple dynamited away rock, installed panoramic windows, and filled the interior with tasteful low-key furnishings, always taking care not to destroy the buildings' rustic feel.
Now, with its arresting views of the fjord and mountains, the hotel has become one Norway's most sought-after retreats.
Brown said that before it closed for renovation and extension a few years ago, his hotel had ranked first in Norway on the hotel review website Trip Advisor.
Gates, who is holidaying with his wife Belinda and their two children, appeared to have a good rapport with his royal hosts, who he knows through the international philanthropy circuit.