Housebuilder Places for People is selling Cotton Court, off Church Street in the city centre for offers in excess of £1m.
Robert Pinkus & Co has been retained to carry out the disposal of the 1857 building which offers 7,104 sq ft over six floors and a basement.
Places for People is moving to new premises at the end of this year.
Danny Pinkus, partner at Robert Pinkus & Co, said: "This is an amazing opportunity to own the freehold of a city centre office location. In light of the development of the Tithebarn scheme and other planned retail development for this quarter of the city, this period building will be based at the heart of all the chic and stylish new bars, shops and restaurants and the attractive position it currently occupies is going to improve in the desirability stakes.
"Opportunities to buy period feature buildings with good quality interior finishes like this one do not come up very often and we are expecting high interest in the property."