Andrew Baxter's remarks came after Alt na Reigh in Glencoe was vandalised for the third time over the weekend. Orange paint was sprayed on the walls of the cottage, while last month stones were thrown at it and later "Jimmy the beast" daubed on a wall.
Savile, who died last year aged 84, may have abused hundreds of young girls and some boys over four decades.
Mr Baxter said locals should decide the fate of the house which Savile bought for £125,000 in 1998 and said demolition was an option.
Savile's assets, including the cottage, are frozen pending legal claims by alleged victims, but Mr Baxter added: "I am writing to the charitable trust which still owns the cottage to get clarification. I am also going to suggest they consider transferring the building to one of the local community trusts in the area as an option."
Savile's trustees had talked about making it into a respite home, but the charity involved in the plans has since closed.