Prime Minister Anthony Albanese will release advice from the solicitor-general on Tuesday on whether Scott Morrison's decision to secretly appoint himself to five ministries raised any legal issues.
Cabinet will discuss the advice before it is released.
In a statement, an Office of the Official Secretary to the Governor-General spokesman acknowledged administrative appointments "were not communicated" by the government.
"The office supports a more transparent process to ensure that any appointments made under section 64 (of the Constitution) are made public," the spokesman said.
"Noting that these reporting responsibilities are the prerogative of the government of the day, the office will await the recommendations of the current process before commenting further."
It comes amid growing calls for an inquiry into the former Liberal prime minister's decision to secretly appoint himself as a joint minister in the health, finance, treasury, home affairs, industry, science, energy and resources portfolios between March 2020 and May 2021.
One of his decisions, as joint resources minister, was to block the PEP-11 gas exploration licence off the NSW coast after the then resources minister Keith Pitt approved the project.
The final decision is now the subject of a Federal Court appeal.
Mr Albanese said questions needed to be answered about Mr Morrison's ministries.
"There is a basic fundamental weakness in checks and balances - if no one knows who the minister is, then how can they be held to account for decisions which are made?" he said.
"There is a question of legality. There hasn't been a suggestion of illegality but there have been questions raised about how this could occur, how it fits in with the conventions."
Greens leader Adam Bandt wants an inquiry to examine Mr Morrison's conduct and whether he misled the parliament or pressured the governor-general or public service.
"The longer that this goes on, the more questions that are raised about exactly how much damage has been done to Australian democracy," Mr Bandt told ABC News.
The Greens have already asked House of Representatives Speaker Milton Dick to refer Mr Morrison to the powerful privileges committee over the scandal.
Mr Bandt said an inquiry would also need to examine who was asked by Mr Morrison to keep his ministries secret from the public and most of his colleagues.
Liberal MP Bridget Archer said she would also welcome an inquiry into the conduct of the former prime minister.
"Australians generally agree that we don't want to see this sort of situation occur into the future, so we need to examine how we got here and how we stop it happening going forward," she told ABC Radio.
Ms Archer said while she was reluctant to ask for other MPs to resign, the former prime minister should "reflect" on his behaviour.
Opposition frontbencher and former Nationals leader Barnaby Joyce said while Mr Morrison should not have taken the action, he had not done anything illegal and it did not warrant him being forced out of parliament.
"Under section 64 of the constitution, he was entitled to do what he did and he did it," Mr Joyce told the Seven Network.
