A private contractor is being sought who would redevelop and manage the 360,000sq ft building, and turn a large part of the site over to commercial use.
Treasury officials ruled out the likelihood of sharing space with burger bars as the redevelopment would face the strict guidelines covering listed buildings.
Cuts at the Treasury mean the building is far too big for the remaining 1,100 staff, who would relocate while the building work was carried out.
Designed by John Brydon at the turn of the century, the building is in a poor state of repair and the cost of refurbishment is estimated at between £100m and £200m.
Office space in the building is likely to be increased and property experts believe that such a prestigious building could command premium rents of well over the £200 per sq ft charged in the area today.
Kenneth Clarke, the Chancellor, is due to announce the plan this morning at a conference marking the first year of the Private Finance Initiative. The PFI, the brainchild of Norman Lamont, the former Chancellor, aims to mobilise the private sector to finance public projects such as roads, prisons and the National Health Service.
Mr Clarke is thought to favour selling the site's freehold, but the Treasury is also considering whether to sell it on a long lease of between 100 and 150 years.
A shortlist of potential buyers will be drawn up in June, with a decision announced by October. Work on the redevelopment is due to start in 1998, and completed by the end of 2001.