Plymouth City Council is to close a number of buildings as part of a plan to cut £10m from its £600m budget.
Four buildings leased by the council, Ballard House, Dean Hill in Plymstock, Fairbairn House and Pearl Assurance House, will be vacated.
Hundreds of staff will be moved to the Civic Centre and Midland House in the city centre and Windsor House in Derriford.
The council said no decisions had been taken on jobs.
Councillor Ian Bowyer, Cabinet Member for Finance, Property, People and Governance, told BBC News: "We are looking at smarter ways of working.
"We have numerous outlying buildings which are soaking up resources.
"I would like to see our priority on the delivery of front-line services."
He said the council was facing a "double whammy" of increased costs and cuts in spending in the government's spending review, due in October.
"We all know that spending reductions are coming in the autumn," he said.
"I want the council to be ahead of the problem, rather than be swamped by it."