Members of the Liberals' decimated moderate faction are swinging in behind Melbourne-based senator Jane Hume to become the party's deputy leader, as it reels from the loss of a swag of heartland seats to progressive female independents.
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Former environment minister Sussan Ley has also emerged as a leading contender after another option pulled out of the race.
The leadership speculation comes as the internal fight over the Liberals' future direction intensifies, with moderate senator Andrew Bragg urging the party to return to its core values of enterprise and fairness.
Senator Bragg will on Wednesday unveil a 10-point policy agenda, which includes higher emissions-reduction targets, a modernisation of the tax system and "largely" free childcare for three- and four-year-olds.
Former Defence Minister Peter Dutton is widely tipped to be installed as opposition leader, after Josh Frydenberg's defeat in Kooyong cleared the path for the Queensland conservative heavyweight to assume the Liberals' top job.
But it's less clear-cut who will be his deputy.
Three Liberal sources confirmed to The Canberra Times that former superannuation minister Jane Hume has strong support among moderates, and could get across the line with the support of some conservatives.
As a woman who lives in Melbourne, Senator Hume is considered the right type of candidate to start rebuilding the party's standing in electorates where it was smashed by so-called "teal independents".
The Liberals lost six blue-ribbon inner-city seats in Sydney, Melbourne and Perth to female independents campaigning on stronger action on climate change, political integrity and the treatment of women.
The party also lost Katie Allen's seat of Higgins to Labor, and is poised to do the same with Trevor Evans' seat of Brisbane.
Two of the Liberal moderates to survive the wipeout, Bridget Archer in Bass and Angie Bell in Moncrieff, have not ruled out a tilt at a leadership position.
Ms Ley has also left the door open, after not only retaining her south-western NSW seat of Farrer at Saturday's election, but extending her margin by more than 2.5 per cent.
Ms Ley has held senior positions in government and opposition during her more than 20 years in Parliament.
Her record was blighted by an entitlements scandal, which prompted her resignation from the Turnbull ministry in 2017.
South Australian senator Anne Ruston, who would have been health minister had the Coalition been returned, is also considering a run at the deputy's position.
Former home affairs minister Karen Andrews had been seen as a possible contender, but pulled out of the race late on Tuesday.
The Coalition's devastating election loss has ignited a fierce internal debate about its future direction.
Some conservative Liberals and Nationals argue the Coalition needs to swing further to the right, while moderates believe it needs to reposition itself in the centre.
Senator Bragg on Tuesday said the party had spent too much time during the election focused on divisive social issues, describing the controversy surrounding Katherine Deves' candidacy as "very regrettable".
"I think people want the Liberal Party to focus on enterprise and fairness and the protection of minorities, rather than try and import US-style culture wars," he told ABC's RN Breakfast.