The prime minister has received advice from the solicitor-general about what portfolio responsibilities he might need to strip from Porter while he sues the ABC for defamation.
Morrison has also sought advice from his department in relation to the attorney-general and ministerial standards.
Labor has asked Morrison whether he is preparing to make Porter a “part-time minister” or drop him altogether.
The prime minister did not rule out either option during Question Time on Wednesday.
“I am considering that advice with my department secretary in terms of the application against the ministerial guidelines,” he told parliament.
“When I have concluded that assessment I will make a determination and I will make an announcement at that time.”
Porter has launched legal action against the public broadcaster over a story about rape allegations against a senior minister.
The attorney-general was not named in the story but his lawyers claim Porter was easily identifiable.
He later came forward to reveal he was the minister in question.
Porter is due to return from stress leave on March 31.
Sex assault report ‘highest quality’: ABC
As the ABC squares up for a defamation case with the attorney-general, the broadcaster’s managing director says the story in question was of the “highest quality” journalism.
David Anderson appeared before a Senate estimates hearing in Canberra on Tuesday and warned senators not to ask detailed questions about the Christian Porter case.
But he used his opening statement to defend the ABC’s report.
“I am confident that the journalism was of the highest quality and that this will be borne out in the court proceedings,” Anderson said.
“We will defend the case and our reporting, which we believe is in the public interest,” he added.
“At all times I believe the ABC has acted in accordance with its statutory obligations of impartiality and its charter in its reporting.”
Anderson said the story regarded an anonymous letter sent to senior federal politicians across the political spectrum, who then forwarded the correspondence to police.
“No reputable media organisation could have ignored the existence of the letter or the fact politicians on both sides of the dispatch box had referred it to police,” he said.
“We did not name or identify the cabinet minister mentioned in the material.
“The attorney-general continues to be entitled to the presumption of innocence and the public broadcaster has reflected this in its reporting.”
Labor pursued the “hopeless conflict of interest” at a parliamentary hearing in Canberra.
Senator Murray Watt listed Porter’s portfolio responsibilities including the administration of criminal justice, issuing ASIO warrants, courts and tribunals.
“There’s barely any role that Mr Porter is not conflicted from. How can he remain as attorney-general?” the opposition frontbencher said.
“How is it possibly tenable for Mr Porter to remain as attorney-general of this country when he has such serious clouds to perform most of his duties?”
Acting Attorney-General Michaelia Cash said the prime minister would carefully consider the solicitor-general’s advice.
Under sustained questioning, Senator Cash continually referred to the legal advice and promised Morrison would respond appropriately.