Sydney radio presenter Alan Jones, avowed conservative and harsh critic of Prime Minister Malcolm Turnbull, took to social media to drop a bombshell.
A News Corp Australia poll showed Bishop is the preferred leader for the party with 34 per cent of votes, followed by Turnbull at 30 per cent, Tony Abbott at 17 per cent and Peter Dutton at 10 per cent.
Mr. Turnbull narrowly survived a vote against a senior government colleague on Tuesday, but is now likely to face a second leadership challenge, reports the BBC.
Three senior Cabinet ministers have told Prime Minister Malcolm Turnbull he doesn't have support and should hold a leadership ballot quickly.
Mr Turnbull's allies said Mr Dutton had not secured the signatures of sufficient MPs to force a second vote.
While this predictable political push for an early election appears unlikely to succeed, the expected demise of the Turnbull government is likely to see another major ministerial reshuffle, with supporters of the successful candidates likely to win key cabinet portfolios.
There is not a shred of evidence on the public record that a Dutton prime ministership would make the slightest difference to the slide in public opinion being suffered by the Coalition in Queensland, as reflected in the LNP's ghastly result in the Longman byelection.
"I was wanting to continue to support Malcolm Turnbull for years to come as leader of the Liberal Party".
A clearly exasperated Mr Hogan also said he had discussed his decision with the deputy prime minister and leader of the Nationals, Michael McCormack.
If he became prime minister, Dutton said he would focus on lowering electricity prices, cutting immigration to ease population pressures and boost water investment to help drought-stricken farmers.
Mr Turnbull won the party-room vote 48-35 but the narrow margin of the victory made another challenge nearly certain in a country that has earned a reputation for a revolving door of political leaders, with six prime ministers since 2009.
He is yet to publicly respond to the latest threat to his rule, although broadcaster ABC reported that he turned down the demand for another party meeting during the phone call.
Apart from anything else, the Liberal Party is so bitterly divided, the wounds so deep, its credibility so shattered, it will take years for the scars to heal.
Attorney-General Christian Porter referred the matter to the government's top solicitor on Wednesday evening - just as Mr Dutton's supporters were circulating a petition and preparing for an imminent leadership challenge.
"There will be no question time today because they don't know who their ministers are. they don't know who their prime minister is", he thundered across the chamber.
Australia has had years of political instability since Prime Minister John Howard lost power in 2007 after more than 11 years in office.
In Question Time on Wednesday, Labor asked the prime minister if he would support a referral.
Dutton may be in breach of the Constitution because of his family's interests in two child care centres.
The opposition Labor Party has gleefully watched the Liberals internal conflict deepen, with the growing prospect of an early election. The movement has been led by the hardline conservative Peter Dutton, 47.
Dutton was ultimately unsuccessful in the first instance, but the fact he only lost by a small margin 48-35 was considered by many as a fatal wound for Turnbull.