The building at All Na Rai Cottage in Glen Coe sparked a fire on Saturday evening, leading to the closure of the A82.
Firefighters put out the flames and roads resumed on Sunday.
The Highlands Council previously granted permission to demolish the site and replace it with a new home.
The site has been abandoned for years and has been repeatedly destroyed since Savile's death in 2011, with his revelation as a prolific sex offender.
A spokesman for the Scottish Police said:
“A inquiry is ongoing to establish a complete situation.”
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