Prime Minister Scott Morrison says he is taking the matter of his stood-aside education minister "extremely seriously".
Mr Morrison received a report into Alan Tudge on January 28, but has yet to announce any action.
The report by former intelligence specialist Dr Vivienne Thom stemmed from an allegation by Mr Tudge's former staffer Rachelle Miller last year of emotional and, on one occasion, physical abuse while the pair had an affair.
The education minister, who intends to recontest his Victorian seat of Aston at the federal election, strenuously denied the allegations and went on leave in December while the investigation was conducted.
Ms Miller refused to participate in the inquiry on the grounds its terms of reference and timeframe guaranteed a narrative that suited the government's agenda.
Ten News reported on Tuesday Dr Thom's report did not support Ms Miller's allegations of abuse.
But the investigation found Mr Tudge had sought to promote Ms Miller from media adviser to senior adviser while they were in an undisclosed relationship, in breach of the ministerial code of conduct.
Ten News said this reason would be used by Mr Morrison to justify Mr Tudge's sacking from the frontbench.
Asked whether he had confidence in his minister, Mr Morrison told parliament on Wednesday: "The matters relating to the minister for education I have been taken extremely seriously."
"The matter is in process and has not concluded and in fairness to all involved in this matter, it would not be appropriate to make further comment at this time," he said.
Labor sought to ask why the minister's parliamentary office name-plate had been removed, but the question was ruled out of order by Speaker Andrew Wallace.
"It is advice from the prime minister's office that causes the parliament to put the names of ministers on doors," opposition business manager Tony Burke said.
Deputy Prime Minister Barnaby Joyce earlier expressed concerns about the leaked report.
"If you're deliberately handing over information that's supposed to remain private ... then you're deliberately trying to make that task in the next election more difficult," he said.
