Chapel Court - which is on Market Street, Queen Street and Castle Street - will go under the hammer on December 8.
The 18,784 sq ft building houses the Job Centre Plus and Merkur Slots and generates £145,966 per year in rent.
The freehold sale will not affect the location of the Job Centre, which has a lease until 2028 via the Secretary of State for Communities which has been based at the site since 1994.
Meanwhile Merkur Slots, which moved into the old William Hill part of the building last year, has a lease agreement until 2035.
The city centre building has been touted as an "excellent investment" by auctioneers Bond Wolfe.
Ian Tudor, joint managing director auctions at Bond Wolfe, said: “This property occupies a prime position in Market Street, with frontages along both Queen Street and Castle Street, in the heart of Wolverhampton city centre.
"We are delighted to be offering the prime freehold of this property for sale at our next auction; it is an excellent investment offering future redevelopment potential – subject to obtaining the necessary planning permissions of course.
"We are expecting considerable interest from a wide range of bidders and property investors.”
The three-storey end-terrace property is described as "well presented throughout" and includes a service yard at the back which can be accessed from Castle Street.
The auction will be live-streamed on Bond Wolfe's website with remote bidding by proxy, telephone or internet only. It will start at 9am on December 8.
For more details and to register to bid visit the Bond Wolfe website, email email@example.com, or call 0121 312 1212 or 01902 928 510.