The deal between the club and the now-defunct Land Development Agency saw the government pay the club $3.55 million for a block of land on Rosevear Place, housing the local CFMEU branch office.

In return, the Tradies club agreed to buy the carpark beside its premises for $3.2 million, and the government also paid the club $49,500 for the nearby old Downer Club site on Hawdon Street.

While the government has paid the club for the Rosevear Place block and old Downer Club site, settlement on the carpark land was delayed until the redevelopment of a nearby carpark into a Coles and apartment block was completed.

The government also allowed the CFMEU to remain rent-free in its Rosevear Place premises for 42 months, due to the delayed settlement for the carpark block and the cost of maintaining the land.

Auditor-General Dr Maxine Cooper on Thursday announced she had now begun a "performance audit" of the tender process for the sale of the carpark land [Block 30, Section 34, Dickson], to the union-linked club.

Dr Cooper said the audit would examine whether the government's tender process for the sale of that specific block was "effectively conducted".

But the scope of the audit office's investigation will also examine "the circumstances associated with the resulting exchange of ownership of three parcels of land" that were part of the December 2014 deal.

Those blocks, in addition to the Tradies carpark land, are: the land currently hosting the CFMEU headquarters and Stockade gym [Block 6, Section 72] and the site of the former Downer Club on Hawdon Street [Block 25, Section 72].

Valuations have previously put the carpark block at $3.18 million, based on constructing a six-storey building and the CFMEU block at $3.25 or $3.55, based on 18 months rent-free or vacant possession.

The old Downer Club site was also valued at $45,000, based on its current lease allowing only a club and carpark, despite the block having an unimproved land value of $725,300.

CFMEU ACT secretary and director of the Tradies Club, Dean Hall, has previously described the deal as "a win-win" for both parties.

He said on Thursday the club would be happy to assist with the investigation.

The deal has been hotly debated in the Legislative Assembly, with the Opposition and Greens earlier this year voting to force the government to publicly release key documents to shed more light on the arrangement.

Those documents could include everything from sales contracts to land valuations and may reveal any potential involvement of government ministers in the deal.

Planning Minister Mick Gentleman has previously said the government entered into the deal because the land, when combined with other government-owned blocks in Section 72, gave it a 'significant urban renewal opportunity'.

Mr Gentleman has also said the documents would be released once they had been checked for commercial-in-confidence and other "confidential" information.