Sheriff Lamont Smith stopped short of labeling the fire as arson. But he did say the fire that destroyed two, wood-building complexes was "suspicious."
"There's not a lot of evidence left when it's a total burn," said Smith.
The fire was reported Friday by a witness who said he saw a tan-and-white pickup containing a man and a woman driving from the scene of the fire.
Chief Deputy Tracy Glover said the witness also provided investigators with additional information.
"There are some people we want to talk to, though we're not calling them suspects at this time," Glover said.
He said it appears fires started separately in each of the two buildings.
The buildings - including saloons, a barber shop and a post office - were built by volunteer labor at a site to replicate original structures constructed in 1962 at the old Paria Town site for the movie "Sergeants 3," starring Frank Sinatra and Sammy Davis Jr. "The Outlaw Josie Wales" also was filmed at the site now located on the Grand Staircase-Escalante National Monument.
The original buildings were torn down after being undercut by a flash flood in 1998.
In 1999, an architect drew plans of the original movie structures. Volunteers from the region - including Kanab, St. George, Richfield, Cedar City and northern Arizona communities - constructed the buildings on higher ground with materials donated by the Bureau of Land Management.
Kanab resident Robert Houston, who helped organize the volunteer effort, said Monday he was devastated by the news of the fire and perplexed at what would motivate anyone to torch the site.
"You can't print what I thought when I heard about it," said Houston. "There's a lot of sweat equity from the community invested in the project."
Houston said he hopes to get together with the BLM and discuss rebuilding the structures.
"There's a lot heritage connected with the movie industry out there," he said.
BLM spokesman Larry Crutchfield said the site was popular with tourists who liked to take pictures of themselves in front of the buildings.
Crutchfield said the site is still open, and the interpretive panels explaining the area's history were not burned.
"I just can't see why anyone would do this," he said.