In an address to the National Press Club in Canberra on Tuesday, Mr Bandt will make the case for government to be at the centre of Australia's coronavirus recovery.

The Morrison government used last Tuesday's budget to lay the groundwork for a private sector-led recovery, aided by billions of dollars in government wage subsidies and tax breaks.

However Mr Bandt will argue an expansion of the public sector was needed to help Australia rebound from the virus without leaving women behind or destroying the environment.

He will also accuse the government of outsourcing Australia's recovery.

"In short, the recovery must be green, pink, quick and safe. Fortunately, we have at our disposal a means of quickly providing [those] jobs ... it is called government," he will say.

"Right now, the most efficient way of creating jobs to get us out of this economic crater is to directly employ people. We don't need to go through big corporations or hope that money will eventually trickle-down."

Unionists had previously called for a boost in government jobs to help the country's coronavirus comeback.

The Community and Public Sector Union urged the Coalition to double next year's grad intake to create 1400 new jobs for young people, who have demographically been one of the hardest hit groups during the pandemic.

Mr Bandt will also say privatisation had been a "demonstrated failure".

Based on an analysis of the budget papers, the Greens estimated taxpayers would pay private entities $52 billion over the next year for services like aged care, private health care, public service contractors and employment services.

The party will seek support from the crossbench to set up a "wide-ranging" inquiry into outsourcing.

"This will be the first ever comprehensive inquiry into four decades of privatisation, contracting out and deregulating essential and public services," Mr Bandt will say.

"The review will help make the case for bringing some essential services back into public and community hands."

It is not the first time in this parliament the Senate will consider problems with outsourcing.

A Labor-dominated inquiry into the impact of contracting out government programs in February called for an end to outsourcing services that dealt with complex cases and vulnerable people.

The committee heard the outsourcing of more than 2700 Department of Human Services call centre jobs led to more mistakes, delays and service disruption.

The inquiry also urged for the average staffing level cap on the public service to be lifted immediately.

Coalition senators on the committee filed a dissenting report, saying the cap "has huge value as it forces agencies to identify opportunities to reprioritise staff time before seeking costly new resources".

"This rule also has the benefit of forcing agencies to regularly hone their strategic focus," the senators argued.

The government confirmed last week the thousands of extra jobs added to the ranks of the federal public service to deal with the COVID-19 pandemic will not be a permanent fixture, with the cap set to stay in place for the foreseeable future.

However the government will introduce a whole of government procurement panel for consultants, a move that is expected to get better value for money and increase transparency.