The site, located at 1 Stewart's Place, partially collapsed last month.
However, Alliance Councillor Andrew Muir said the owner has yet to secure the site.
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He said: "The closure of part of Bangor Road has inflicted weeks of disruption upon the people of Holywood - the owner should not have allowed the building to deteriorate into the perilous state it currently is in.
"Instead it is dragging on and we are hearing more and more broken promises about its future. While we would ideally like to save the building, sadly as this issue continues, it's looking more likely that demolition may now be the only viable option."
(CD)
