Representatives from building services company Rok have been in talks with Bristol City Council after the firm's collapse left contracts in doubt.
The Exeter-based company held a number of contracts with the authority, including one to build 12 new council homes.
Administrators PricewaterhouseCoopers announced 711 job cuts at Rok, which employs about 4,000 people.
Both Rok Plc and Rok Building Limited went into administration this week.
Rok, which has contracts throughout the West, provides building services for councils, schools, housing associations and businesses.
Building work at the council's Croydon House in the St Lawrence area of Bristol has been halted, and scaffolding left up.
One resident said she felt like she was living in a "prison cell".
"I'm just depressed, it gets you down," she said.
"You don't see daylight."
A spokesman for Bristol City Council said Rok was one of the main contractors it used to install kitchens, new wiring and windows in its council properties, and for major work to some of its high-rise buildings.
"We have been holding discussions with representatives from Rok as they have withdrawn from all current construction sites," he said.
"However, we are unable at this time to confirm whether they will no longer be carrying out this work for Bristol City Council.
"A statement is expected from the administrators on Monday and we will be reviewing our position."