A Senate inquiry into political interference at the ABC will come a step closer on Monday, when the Greens propose draft terms of reference.

The proposed inquiry would examine the sacking of the managing director Michelle Guthrie, the conduct of former chairman Justin Milne and the board, the system of board appointments and any political influence or attempted political influence over editorial matters.

Milne was forced to resign last month in the face of damaging allegations he compromised the independence of the public broadcaster by demanding journalists be sacked, but he denied there had been any interference by the government in the ABC.

If the inquiry wins the support of Labor and the crossbenchers it will bring to five the number of inquiries the ABC is facing.

There is an efficiency review, a competitive neutrality inquiry, a departmental investigation ordered by the communications minister, Mitch Fifield, and an inquiry by the ABC board itself into the Milne allegations.

The Greens draft includes a proposal to call Fifield, the ABC board and Milne as witnesses.

Last month the Greens joined forces with Labor to call for a parliamentary inquiry, and they have in-principle backing from key crossbenchers including the Centre Alliance and the independent Tim Storer. Labor’s communications spokeswoman, Michelle Rowland, is drafting her own terms of reference to be put to the Senate later this month.

The Greens media spokeswoman, Sarah Hanson-Young, will ask the Senate to refer the ABC matter to the environment and communications references committee for inquiry and report by 29 March.

“We know something has gone terribly wrong at a board level at the ABC,” Hanson-Young said. “While dedicated staff and journalists continue doing their jobs, senators across party lines also need to rise above the politics and get to the bottom of what is going on with the ABC.

“The objective of this inquiry is to find solutions to what has clearly become an issue of political interference. We must work together to help fix the problems of political interference and restore genuine independence at the ABC, as the Australian people, and our laws, expect.

“Until we have transparency and clarity over what has happened and the extent of the political interference, a cloud will remain over the ABC’s future independence.”

Rowland, who said last month a Senate inquiry was necessary because the “independence and integrity of Australia’s most trusted news organisation” were at risk, has been talking to stakeholders about the terms of reference.

“The ABC does not belong to the Liberals – it belongs to the Australian people,” Rowland said.

The ABC section secretary for the Community and Public Sector Union, Sinddy Ealy, said an independent Senate inquiry was essential, because the departmental review was flawed.

“And we need terms of reference that address all of the levers that governments use to politically interfere with the ABC, including cutting its funding, subjecting it to a barrage of inquiries and reviews, editorial complaints, stacking the ABC board and inciting culture wars,” she said.