An offer has been submitted for Bayard Place in Broadway.
Peterborough City Council had put the offices on the market with an asking price of £6.2 million as it is moving staff to the new Fletton Quays development on Peterborough’s South Bank.
A council spokesman said: “We are currently in the process of negotiating to sell the building. It is under offer and we hope to be in a position to make a formal announcement shortly.”
Bayard Place is currently used by the council for services such as housing.
It has a ground floor and four upper floors, together with an underground car park for 129 vehicles.