Immigration Minister Peter Dutton has refused to deny rumours he offered to resign his post via text message.
Mr Dutton was a vocal supporter of former Prime Minister Tony Abbott in the lead-up to his ousting on Monday night and was behind a number of embarrassing gaffes for the Government in the past few weeks.
After Malcolm Turnbull was appointed Prime Minister on Tuesday, Sky News reported Mr Dutton offered to step down from his post.
But Mr Turnbull refused to comment on ministerial arrangements when questioned on Wednesday.
“You don’t have long to wait,” he told reporters in Canberra.
“I expect the new ministry, with some changes, to be sworn in on Monday.”
The Immigration Minister provided the Government with two damaging blunders this month.
In early September, he accused Fairfax Media and the ABC of waging “jihad” against the former Abbott Government.
This was followed by the broadcast of a “private conversation”, recorded by a boom microphone positioned above Mr Dutton, Mr Abbott and Social Services Minister Scott Morrison as they waited for a press conference on Syrian refugees.
Mr Turnbull also said on Wednesday that he was keen to see the number of female MP’s in cabinet increase.
“There is no greater enthusiast than me for seeing more women in positions of power and influence in parliament, in ministries right across the country,” he said.
“I can assure you that. I am very committed to that.”
Treasurer Joe Hockey might be one who loses his job in Mr Turnbull’s cabinet re-shuffle, with Mr Morrison linked to the position.
“I’ve had discussions with the prime minister. We’ll leave it at that. We’ll see what happens,” Mr Hockey said.
It also emerged on Wednesday that US President Barack Obama phoned Mr Abbott to offer his commiserations.
The ABC report that Mr Obama thanked the ex-PM for his service and praised him as a “very good mate on many important issues”.