Prime Minister Malcolm Turnbull has declined to say whether Mal Brough has offered to step aside from the front bench.
Mr Brough is facing a police investigation into whether he asked James Ashby, a former staffer of Peter Slipper, to copy the former Speaker's diary.
The special minister of state told parliament last week that he did not make the request of Mr Ashby, despite saying in a television interview last year that he did.
Mr Turnbull told the ABC's 730 program on Monday that Mr Brough had clarified his position in parliament.
"He has set out to explain it," Mr Turnbull said.
"I really don't want to go into the ins and outs of Mr Brough's remarks, but certainly it's an issue we are all very keenly aware of."
Asked whether Mr Brough had offered to step aside, Mr Turnbull said: "I don't want to go into discussions between myself and ministers on this or any other matter."
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