SNP Councillor Ruairi Kelly met with the owner and architect of the former Prince and Princess of Wales Hospice at Carlton Place on Monday.`
A blaze engulfed the B-listed property in the Gorbals area earlier this month, which police believe may have been started deliberately.
There are now fears about the property deteriorating further.
Commenting on his meeting over the future of the historic building, councillor Kelly said: “We have been out at Carlton Place talking to the owners and the architect of this building following the most recent fire.
“We stressed the importance of getting a temporary roof on as soon as possible to protect the fabric of the building and asked them for a workplan for what they are going to do for the renovation and most importantly the early work of getting protections in place.
“We did stress that very strongly.”
The city convener for neighbourhood services and assets said if action doesn’t take place the council would step in.
He said: “If they weren’t going to do it very soon we would have to look at other measures with the council stepping in and then looking to recoup our costs.
“It is imperative that we protect this building and don’t allow it to go the same way as so many other buildings in private ownership have in Glasgow.”
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We had previously reported in April how there were claims drug users had moved into the privately owned vacant property, which lies off Bridge Street.
The most recent fire was not the first as a smaller blaze took place at the Georgian terrace in January.
Councillor Kelly added: “The finances available to the council for interventions can be prohibitive but I am determined to take a more forceful approach to protecting the built heritage of the city and stepping in at an early stage.”
He continued: “We will then aggressively chase owners to recoup the cost to the people of Glasgow.
“Property owners, GCC included, are all merely custodians of this city for future generations and have a responsibility to both protect and improve its fabric.”