The Greens are expected to request on Tuesday that Speaker Milton Dick consider allowing Mr Morrison to be referred to the privileges committee, which deals with matters such as contempt of parliament.
A royal commission into robodebt made several adverse findings against Mr Morrison, including that he "allowed cabinet to be misled" on the legality of the scheme when he was social services minister.
The scheme, which ran from 2015 to 2019 under the former coalition governments, used annual tax office data to calculate average fortnightly earnings and automatically issue debt notices to welfare recipients.
Hundreds of thousands of Australians were caught up in the debacle, which illegally recovered more than $750 million and was linked to several suicides.
Mr Morrison rejected the adverse findings against him and said they were "disproportionate, wrong and unsubstantiated".
He also accused the Labor government of a "political lynching" and described the commission as a "quasi-legal process".
His comments were slammed by Government Services Minister Bill Shorten, who said Mr Morrison was trying to frame himself as a victim of robodebt when he wasn't.
Mr Shorten described the former prime minister, now a backbencher, as a "bottomless well of self-pity with not a drop of mercy for all the real victims of robodebt".
Mr Morrison is the only former minister singled out in the robodebt report who remains in parliament.
Alan Tudge and Stuart Robert resigned this year, sparking by-elections in their seats.
The Greens have previously sought to refer Mr Morrison to the privileges committee over the secret ministries saga.
The referral was ultimately not supported, but Mr Morrison was censured by the parliament.
23°C