Work has already started to knock down the former Springburn Public Halls, in the north of the city, after it was found to have "significant damage".
Council workers shut off part of Keppochhill Road last week over fears the 110-year-old building could collapse.
The halls on Keppochhill Road were fenced off and the road closure was put in place at Millarbank Street.
Workers made the building secure as an investigation was launched to examine the damage.
Once the decision was made that nothing could be done to save the B-Listed halls, demolition experts were called in and have now started dismantling parts of the building by hand.
Bulldozers are expected by the end of the week.
The building is owned by the council. It is attached to tenement blocks.
A Glasgow City Council spokesman said "Demolition work has already started on the Springburn Halls.
"We hand delivered letters to the residents who live beside the halls.
"In that letter they were told that we might have no option but to demolish the building."
The Italianate-style, red sandstone building was opened in 1902 and from 1960 was used as Springburn Sports Centre.
It was closed by Glasgow District Council due to dry rot problems in 1985 and has lain empty since.