Leicester city councillors want HQ to be demolished
A group of councillors want Leicester City Council's headquarters on New Walk to be demolished.
The two tower blocks house 1,400 staff and were deemed structurally unsafe after an independent inspection.
Councillor Ross Wilmott said despite having the £53m to fix the problem, he did not think the buildings were worth repairing.
Local businesses said they fear a loss of trade if the building is demolished and the council moves elsewhere.
One businesswoman said: "It would be detrimental to businesses in the area as a lot of our clients are from the council."
Deputy Mayor Rory Palmer said that no decision would be taken until the end of the year.
He said: "A number of decisions have been considered and explored. We have a desire to keep the council headquarters in the city, we feel that's important and that it is accessible to the public."
The authority has been based at New Walk for more than 30 years but its concrete structure has begun to crumble and it is now seen as an increasing safety issue.
In early 2010, structural engineers told the authority the tower blocks needed urgent repairs.
Mr Wilmott is a member of the city council's scrutiny committee, which met to discuss the problem last week.
He said: "We have the money to do the work on the buildings. But once you start working on an old building you start to find more and more problems."