Attorney-General Christian Porter has said he will make a decision on the future of the head of Border Force, Roman Quaedvlieg, within weeks.

Porter also said that Prime Minister Malcolm Turnbull had asked him to be the decision-maker.

This follows detailed questioning in Senate estimates hearings this week about the investigation of an allegation against Quaedvlieg, who has been on leave with full pay for nine months, collecting about A$500,000 in that time.

A federal statutory officer, Quaedvlieg, the man in the military-style “ink-navy” uniform who has had a very high profile as the nation’s chief border cop, was accused last year of intervening over a job on behalf of a Border Force employee with whom he had a relationship.

The government has been extraordinarily secretive when questioned in recent months about where the investigation was up to and why it was so prolonged.

The timeline is a sharp contrast to the Barnaby Joyce affair. Less than three weeks after the scandal broke publicly about his relationship with his former staffer and now partner Joyce had resigned from the Nationals leadership and thus the deputy prime ministership.

Bureaucratic wheels naturally turn more slowly. But this case has been at the extreme end, with its enormous expense to taxpayers who are forking out hundreds of thousands of dollars for a senior official – who is himself highly frustrated at the delay – to do nothing.

Now the Quaedvlieg matter has become so difficult that it has been handed to Porter to make the call on his future.

But when Labor’s Penny Wong in estimates on Tuesday asked the secretary of the attorney-general’s department, Chris Moraitis, under what legislation the attorney-general had authority, he did not know.

“Which piece of legislation, or cabinet decision, gives your portfolio minister the power to make the decision he’s going to make?” Wong asked Moraitis. “I can’t answer that senator,” he said.

Nor could Moraitis provide any enlightenment on who was paying Quaedvlieg’s legal fees or when Porter would make his decision. It is believed Quaedvlieg is meeting his own legal costs.

Porter finds himself on delicate ground. If his decision were adverse and Quaedvlieg (a one-time policeman) took legal action, the government could end up in a high-profile court case.

The allegation was originally referred to the Australian Commission for Law Enforcement Integrity (ACLEI). After ACLEI produced a report last year, the matter was then referred to the secretary of the prime minister’s department, Martin Parkinson.

The secretary of the home affairs department, Mike Pezzullo, told an estimates hearing on Monday: “I received a report in the third quarter of last year at some point. Dr Parkinson and I agreed that with the administrative follow-up, to ensure that natural justice and due process considerations were applied, that matters were best dealt with by him – that is to say, Dr Parkinson”.

Although Pezzullo did not spell it out, the core question is whether Quaedvlieg breached the public service code of conduct.

The length of the timeline led crossbench senator Derryn Hinch to quip: “A competent cop can wrap up a murder investigation in one year”.

In a separate estimates hearing on Monday a deputy secretary of the prime minister’s department, Stephanie Foster, said Parkinson had concluded his inquiry in December and given a copy of that report to Quaedvlieg on December 22. Quaedvlieg replied on January 17. It is believed he had issues with the investigation and analysis.

The material went to Porter on February 5.

Porter said in comments issued by his office: “The prime minister has asked me to consider the report of Dr Parkinson and to assume the role of making any necessary decisions based on the report, rather than the minister for home affairs [Peter Dutton].

"This is to prevent any apprehension of bias given Mr Quaedvlieg’s reporting obligations to minister Dutton under the Australian Border Force Act.

"As a result of this request, and before receiving Dr Parkinson’s report, I sought legal advice from the Australian Government Solicitor to satisfy myself that I can consider and determine this matter. The AGS has confirmed that I am able to procedurally undertake this task.

"I am now considering Dr Parkinson’s report.

"I intend to complete my consideration in a matter of weeks,” Porter said.

Dutton told The Conversation this week: “I’m certain of the fact this has been dealt with in the most expeditious way possible”.

Michelle Grattan does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.