A “safe zone” has been set up around the building, extending to Central Station which will remain closed for the rest of the week.
The council took control of the site from the Scottish Fire and Rescue Service (SFRS) on Thursday and carried out its own assessment of the damaged structure.
Raymond Barlow, from the council’s building standards team, said it was not possible for the council to say exactly which aspects of the building could be saved, nor how long the demolition will take.
He said: “You are talking a good number of weeks before we see any change to aspects around here.
“We need to start work at one end of the site, take off the highest bits of danger and hopefully that will let us start to access parts of the station and get the station back up before coming to the façade.”
The council said crews would work around the clock, but timescales were weather-dependent as cranes cannot be used in high winds.