The suggestion came from council city property manager Kevin Taylor as an investigation continued into Monday's incident, in which a large external glass pane fell from the building in George St.
Mr Taylor said the investigation was examining whether a problem with the glass pane itself, or its attachments to the building, had caused the incident.
Depending on what was found, the council would have to consider a range of options - from extra wrapping to secure the glass, to a beefed-up annual maintenance regime, he said.
If problems were bad enough, or the costs of fixing them prohibitive, the complete removal of the decorative glass facade would also have to be considered, he said.
''That [removal] would be something we'd definitely have to examine. I certainly wouldn't exclude that from our consideration.''
The 6m by 3m glass pane split into two pieces and fell, minutes apart, on to a veranda below, he said.
Council staff cordoned off the area underneath the veranda after the first piece of glass fell, only to witness the second piece fall about five minutes later, he said.
Both pieces fell as large chunks on to the veranda below and shattered upon impact, sending fragments of glass on to the street, as well, he said.
Nobody was injured, but a second large pane of the decorative facade - immediately below the one that fell - was also damaged, he said.
Engineers and glaziers visited the mall yesterday to assess the damage and cover the second, damaged pane of glass in a protective wrap until it could be safely removed, he said.
They also examined the rest of the building's glass facade, looking for a possible cause of Monday's failure.
That included checking for signs of wear and tear where the glass panes were attached to the building, and collecting glass debris from the veranda, which would be tested for faults, he said.
A similar failure inside the mall in 2011 - in which a glass ceiling panel exploded and glass fell on two people below - had been blamed on nickel sulphide inclusion, which could occur during the glass manufacturing process.
Nickel sulphide crystals, formed during glass toughening, slowly reverted to a larger form and expanded to trigger shattering.
Mr Taylor said it was considered ''very doubtful'' the same fault had recurred, but the tests would confirm that.
''It either normally occurs at manufacture or occurs within 12 months, and [the glass facade] has been up there for just on six years now.
''If it's contributing again, then we're going to have to obviously remove what's there and reconsider what can be installed, with a high degree of safety and certainty in mind.''
The council had responded to the 2011 incident - which occurred before Mr Taylor's time with the council - by adding a protective film to each ceiling panel inside the building, at a cost of $60,000.
However, Mr Taylor said the same treatment had not been applied to the exterior glass facade at the time, as ''they are a completely different fixture''.
''It wasn't assumed to be a risk there,'' he said.
Adding a similar treatment to the glass facade would cost more than $60,000, and the council would ''have to investigate whether or not that's going to be required from a risk-management point of view'', he said.
''It's being treated utterly seriously,'' he said.
Council staff expected to know more about what caused the failure, and the possible options to fix the fault, within days, he said.
