The Papua New Guinea newspaper, The Post Courier, says moves are afoot to push for a former deputy prime minister, Don Polye, to be made the prime minister.
The paper says that the change is being driven by another former deputy prime minister, Sir Puka Temu, as parliament is to meet next week to elect a new governor general.
It suggests the sitting be used to present a motion of no confidence as a way of ousting Sir Michael Somare who stepped aside last month pending a possible misconduct in office probe.
Before making Sam Abal the acting prime minister, Sir Michael chose to give the foreign affairs portfolio to Mr Polye, but he has declined to take it up.
The acting speaker has said only the election of a governor general is on the agenda but Sir Puka has told the newspaper, The National, that the opposition will take him to court if he refuses to follow the democratic system of government.
At least 55 votes are needed for a motion to be passed.