Emergency services were called to Allt-na-Reigh cottage in Glencoe at tea time on Saturday.
It is not thought anyone has been injured.
The A82 is closed in both directions as emergency services continue to deal with the flames.
A Scottish Fire and Rescue spokesperson said: “We were called at 17:36 and have three pumps in attendance.”
A Police Scotland spokesperson said: “The A82 is closed in both directions between Tyndrum and Ballachulish Bridge following a report of a fire at a property around 5.40pm on Saturday, 8 February, 2025.”
“Emergency services are in attendance and drivers are asked to avoid the area.”
Jim’ll Fix It presenter Savile was exposed as one of Britain’s most prolific and high-profile sex offenders after his death in 2011.
From 1998 until the day he died, he lived in the bungalow which was built at a beauty spot opposite the Three Sisters of Glencoe.
The building fell into a state of decay following the paedophile’s 2011 death.
Images from inside the lair, where Savile is believed to have abused 20 victims, show collapsed ceilings, smashed walls and piles of debris. At one point, the property was whitewashed in a bid to deter vandals, however, words such as ‘beast’ and ‘paedo’ remain scrawled onto the exterior walls.
Following Savile’s death, the two-bed bungalow was put up for auction and was purchased for £212,000, with the buyer intending to live there. However, it was bought over for a reported £335,000 by the family of Harris Aslam, boss of Kirkcaldy-based convenience stores business Eros Retail.
His plans were initially hit with a flood of objections, including from Heritage Scotland, who said they did not fit the scenic landscape.
The property was then approved for demolition last year to make way for a new four-bed home.