In December, the council served an urgent works notice on the owner of the buildings.
It meant the council could carry out the repairs itself and reclaim the cost if they did not take action.
A council report said: “The owner has declined to do the works, citing a lack of funds and that the cost of the works is disproportionate relative to the heritage significance of the Kirkgate properties as the reasons.”
Talks were held over a sale of 83 to 88-99 Kirkgate to the council, but the owner disputed a valuation of the properties, the Local Democracy Reporting Service said.
As a last resort, council bosses said they could potentially use compulsory purchase powers on the buildings “with a view to them being fully restored and brought back into meaningful long-term use”.
They said the buildings posed no risk to public safety after nearby businesses complained of the impact on their trade.
The building’s owner has been contacted by the BBC for comment.