Several ministers have tendered their resignations.
Opposition lawmakers reacted with outrage when the government shut down Parliament hours early so that Liberal Party lawmakers could focus on their leadership crisis.
Public and some internal Liberal polling suggested that this seat, which adjoins Mr Dutton's electorate of Dickson, would swing towards Mr Turnbull and deliver a devastating blow to Opposition Leader Bill Shorten.
A leadership spill motion is a vote to declare the leadership of a political party vacant, allowing an open contest.
Media reports say other lawmakers are considering running for Turnbull's job, including Treasurer Scott Morrison.
Turnbull did not immediately make a public response.
Bishop was elected unopposed as the deputy leader of the Liberal Party and said she would be surprised if anyone opposed her going forward.
Australia's beleaguered prime minister was resisting pressure to quit as opponents from within his party struggled on Thursday to show that he had lost the government's support. None of them, including two stints for Labor leader Kevin Rudd, have served a full term.
"What is happening right now is the government have decided this place has fallen apart so completely that they are dissolving the parliament for the day entirely", he told the lower house on Thursday.
Australia's continued political instability has fuelled anger and frustration among voters and hindered investment by the business sector. The Aussie was the worst performing major currency on Thursday.
Australian newspapers echoed the frustration many voters feel over the constant leadership changes.
"What we have been seeing in Canberra with leadership changes over the last 10 years, is letting our great country down". Business likes certainty and confidence in what happens in the future. He also criticized Alan Joyce for using his position as chief executive officer of Qantas Airways Ltd.to advocate for legalizing same-sex marriage.
Malcolm Turnbull, Australia's prime minister, speaks during a news conference at Parliament House in Canberra, Australia. Picture taken August 21, 2018.
That legal advice is expected to be delivered to Mr Turnbull at about 8.30am local time and if the Commonwealth's top legal advisor expresses doubts about Mr Dutton's eligibility, that could damage his chances.
Vanstone, a cabinet minister for the entire almost 12 years of the Howard government revealed part of his genius for running the party's broad church so successfully and it's a warning to the Dutton camp to not swing too far to the right.
The former Home Affairs minister has his own legal advice that his interest in childcare centres - which receive a funding stream from the federal government - does not breach section 44 of the constitution.
He also said: "I made it very clear that I believe former Prime Ministers are best out of the Parliament".
Australian shares are down more than 1.5 per cent since the first leadership challenge this week.
"Earlier this morning I called the prime minister to advise him that it was my judgement that the majority of the party room no longer supported his leadership", Dutton had told reporters outside parliament earlier Thursday.