The council is considering relocating its Moray Pl library to the lowest three floors of the former post office, plus extending a new building over Bond St and the adjacent car park.
Council property manager Robert Clark is talking to three parties about the Moral Pl site and said he expected "to have an offer or proposal on the table" by June or July.
The council could go into a joint venture redevelopment or lease the Moray Pl building as a commercial building for offices.
A recently completed costing on redevelopment of the chief post office had been "favourable".