Fawzi Ibrahim, one of four elected trustees tasked with protecting the UCU's assets, makes the allegation in a letter to members of its national executive committee.
Sally Hunt, the UCU general secretary, has denied the claims.
After the UCU was formed from the merger of the National Association of Teachers in Further and Higher Education and the Association of University Teachers in 2006, it decided to sell the unions' respective headquarters in Britannia Street and Tavistock Place in central London and move to new premises in Carlow Street, Camden Town.
In 2008, the UCU took out a £13.4 million bridging loan to fund the purchase of the building while the sales of the Britannia Street and Tavistock Place properties were completed.
An extra £1.4 million was later added to the loan.
The sale of the Tavistock Place property went through in December 2008, allowing £5.3 million of the loan to be repaid.
But although the UCU exchanged contracts with a buyer for Britannia Street in November 2009, the sale has yet to complete due to delays in granting planning permission for student accommodation.
Ms Hunt tells Mr Ibrahim in a letter of response that the outstanding balance on the bridging loan is £9.5 million, while the current Britannia Street contract is worth £12 million.
But some argue that the purchase of Carlow Street and the attempt to sell Britannia Street have cost the UCU too much money - and that the union should simply have moved into the latter property after selling the Tavistock Place building.
The union's accounts state that over the three years to 2009-10, interest payments on the bridging loan amounted to £709,080.
Capital gains tax will also be payable when the Britannia Street property is finally sold.
Mr Ibrahim, a former Natfhe treasurer, says in his letter that taking into account the agents' and legal fees owed once the sale is finally completed, the cost of the deposit for the new HQ and a fall in property values since 2008, "the outcome of the decision to buy Carlow Street is a staggering loss to the union, something in the region of £3m-£4m".
Ms Hunt says in a statement: "The impact of recession on the property market is well-documented. It would be unwise to try to gauge what the financial situation with Britannia Street is until a sale has finally been completed." She adds that having one modern HQ "has led to real benefits for members and our employees".