A blaze ripped-through the building last month causing extensive damage but the main structure was saved.
The art school’s director, Professor Tom Inns, revealed the extent of the damage to Scottish MPs at a Holyrood committee hearing yesterday.
He said the cost could be met by government, insurance and donations.
The BBC reported that Prof Inns told MSPs: “We have been in discussion with the insurance company and a team of people appointed to deal with the immediate securing of the building, and the estimates are probably somewhere between £20-£35m.”
It will take 12 to 18 months to reopen the east wing of the building and 36 to 48 months to reopen the west wing, Mr Inns said.
“The insurance will cover certain things, it won’t cover other things. Obviously it’s a very complex insurance case.
“We will have to raise funds so we will be setting up a fundraising campaign, so I think if all of these things come together we will be able to cover the cost of that restoration.”