If the owners - Conlin Properties - don't comply, the council will do the work themselves and seek reimbursement of the predicted £11,000 costs from the owners afterwards.
At a meeting of Wigtown Area Committee on Wednesday, Billy Murray from the council's planning department said that a "positive" letter had arrived from Conlin Properties claiming that they have already invested heavily in making the structure safe and that they have instructed a local firm to remove growing vegetation from the rooftop of the building.
He added that the firm say they are awaiting tenders from various decorating companies before finalising plans to have the old hotel's frontage painted.
Mr Murray said: "I asked if they could give us a timescale but they weren't prepared to do so.
"I later spoke to an agent on behalf of the company who said that the removal of vegetation is hoped to be completed within 14 days and painting within eight weeks."
He added: "If the work is not done, I made it very clear that the council will gain entry to the property if necessary and will do the work themselves. When they heard the expected costs involved in this, they were quick to assure us they would get it done."
Local councillor Alistair Geddes said that the committee should be wary of the letter as such promises have been made in the past.
He said: "The company have treated the people of Whithorn with nothing more than contempt for the past five years.
"They now write to us saying this work will be done. I don't think we should believe a word of it. I say we impose the enforcement order with the maximum sense of urgency possible."
In agreement, Councillor Graham Nicol said: "It is high time this is addressed and I'm glad we are finally in a position where we can do something."
The notice will be issued and a 28-day period is allowed for Conlin Properties to appeal it, after which the works must be carried out with another 28-day period.