People who work for Gloucester City Council have been told they could face pay cuts to help it save £6.5m over the next three years.
Under a proposal being considered staff are being asked if they would reduce their hours from 37 to 35 a week.
The pro-rata reduction in wages would save the council about £200,000 per year.
A spokesman for the Unison union said any negotiated change in conditions was better than one imposed by management.
Council leader Paul James said there was a trade off between making a reduction in the overall pay bill and the number of jobs it might have to lose.
"So, if we do get the agreement from staff to cut the working week we could protect jobs here," he said.
Under the proposals the council, which is run by a minority Conservative administration, hoped to protect landmarks like the Guildhall and Eastgate Market from budget cuts.
The proposals are due to go before the council's overview and scrutiny committee on Monday then to a full meeting on 25 November.
A Unison spokesman said: "I would question what happens to the work that would have taken place in those two hours?
"Is it going to be left or are staff going to have to work harder?"