It is also the hall where the Beatles were covered in flour by students during a concert in 1964.
Venue owner Bristol City Council advertised the work in the Official Journalin August and hopes to send out tenders at the beginning of next year.
The project was originally expected to cost around £90 million but the plans were scaled back earlier in the year because of funding problems.
When the notice was placed on the Official Journalthe value was around £60 million. That is now believed to have been pared back by a further £10 million and the value may be cut again.
Work has been divided into two phases, down from the three announced in the advertisement. The council is hoping the winning contractor will be able to stay on site to continue with the second phase straight after completion of the first.
The city centre venue, which seats around 1,800 people and was opened in its present form in 1867, will undergo extensive refurbishment, with new build work lined up as well.
Construction will get under way with the demolition of Colston House, next to the hall, in November next year. This will make room for a new foyer on which work will start around six months later.
The first phase is due to be finished in November 2008. An end date for the second phase has not yet been decided.