The Fair Work Commission said it not yet made a court application for an administrator for the embattled division after allegations of organised crime links, but the federal government has warned the union not to fight the move.
Workplace Relations Minister Murray Watt has instructed his department to have legislation ready to table in parliament as soon as it resumes in August if the CFMEU contests any legal order.
The government announced it would put the construction division into administration following allegations of being linked to bikies and organised crime.
"The very first briefing that I received in this new role, within hours of being sworn in, focused on the legislation, where it was at, what further decisions needed to be made to finalise it," he told ABC Radio on Wednesday.
Murray Watt was sworn in as workplace relations minister on Monday. (Lukas Coch/AAP PHOTOS)
"We will support any application that's made by the general manager of the Fair Work Commission to put some of these branches into administration.
"If that application is opposed and there's barriers, if it's not resolved by the time parliament returns, then we will remove those barriers by government legislation."
The CFMEU has appointed former anti-corruption tsar Geoffrey Watson to investigate the criminal allegations.
While Senator Watt said he had respect for Mr Watson as "a very eminent lawyer", but the issues within the union's construction division were so serious it could not be relied on to tackle them alone.
Parliament returns on August 12.
The Fair Work Commission declined to provide any further details on progress on an application for an administrator.
In Victoria, where much of the attention has been focused, state Liberals pushed for a parliamentary inquiry into the union's construction arm in the state.Â
"Victorians are paying a very heavy price financially for this," Opposition Leader John Pesutto said, referring to billions of dollars in budget blowouts on projects he blamed on the construction union.
The Victorian Labor government has announced an inquiry headed by public servant Greg Wilson but the Liberals argue it hasn't been given enough powers, resources and time.
Premier Jacinta Allan said Mr Wilson was welcome to approach the government if he needed more time, resources or information to complete his work. She described the Liberals' inquiry push as a "political stunt" and an attack on workers.
The union also faces allegations of receiving kickbacks from construction companies as payment for being allowed onto worksites.
The Queensland CFMEU is also under fire for causing commuter delays ahead of the state's annual agricultural show, the Ekka, by holding up work on a temporary train station.
Exhibition Station was set to open to transport showgoers but the Cross River Rail Delivery Authority said it was not safe to do so as too many work days had been lost by union strikes.
Premier Steven Miles said it was disappointing the station would not open and that the CFMEU had played a role in it.
"I am disappointed that the Exhibition Station can't reopen for this year's Ekka," he told reporters on Wednesday.
"I understand that because of those delays, there are safety concerns around the timeframe.
"They have to put safety first."
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