An insider at the union said the five-storey office in Wimbledon may be sold to a developer and turned into flats.
The insider added that negotiations over selling the union's national training college in Manchester were well advanced. The campus at Whalley Range is a listed building and has run up large maintenance and running costs.
It is understood that there may be more than 100 redundancies as part of the retrenchment package.
The insider said: "It is well documented that the union has financial difficulties. Now that the redundancy notice has been sent to the Department of Social Security, a plan to try to limit the number of redundancies has been formulated, which includes the sell-off."
He said that 20% of the union's property portfolio around the country was not in use.
The union, which has 700,000 members, recruited 14,000 more members last year but has battled with high overheads.
Phil Davies, GMB regional secretary for construction, said the sale would have little impact on the service the union offered.
The GMB was unavailable for comment.