The owners of the Egyptian Halls, built by Alexander 'Greek' Thomson, are said to be close to finalising a hotel deal that could ensure the preservation of the A-listed building in Union Street, opposite Central Station
The halls, completed in 1872, are recognised as the finest surviving example of Thomson's commercial buildings.
A source said there had been a "significant" development in the plans.
A new planning application is expected to be submitted to Glasgow City Council later this month.
Last year, the halls' owner, Derek Souter, boss of Union Street Properties, said he had no option but to demolish the building because renovation costs had risen to £20million.
Thousands of people backed a Facebook campaign and petition to save it from the axe and a new post on the campaign page says: "The owners are very close to agreeing the hotel deal that would underpin the 100% preservation of the Egyptian Halls."
One supporter said: "Here's hoping the halls can inspire a new generation of Glaswegian architects to make such excellent buildings."
The building has been lying empty for more than 30 years and is in poor condition.
A spokesman for Historic Scotland said: "Egyptian Halls is one of Glasgow's most important buildings.
"It has been underused for many years and we strongly support any scheme that conserves, re-uses and celebrates its unique place among the city's superb collection of historic architecture."
It is hoped the renovation could act as a catalyst to the rejuvenation of Union Street, which has been in decline for a number of years.
A spokesman for the city council said a planning application was anticipated.
Union Street Properties and sister company Union Street Investments have so far spent £5m on the project.
The city council previously agreed a £1m grant and Historic Scotland a grant of about £1.65m.