Former Liberal leader John Hewson fears an independent could take Malcolm Turnbull's blue ribbon seat of Wentworth when voters go to the polls for the crucial by-election on October 20.
While the Liberals have held the seat since the party's inception in 1944, there's no guarantee the government will win after the Canberra bloodletting which replaced Mr Turnbull as prime minister.
Pundits believe a strong independent candidate could succeed, meaning the coalition would lose its majority in the federal parliament.
"You'd be foolish to underestimate the significance of the climate issue in relation to that constituency," former Wentworth MP Mr Hewson said on Wednesday.
"It's not going to be too difficult for a significant named independent, with strong credentials on climate, for example, to take that seat in a by-election where there's already going to be a very substantial protest vote against the government."
Liberal powerbrokers in Canberra are also pressuring Wentworth preselectors to pick a woman after former frontrunner Andrew Bragg dropped out of the race on Monday.
Independent Licia Heath has declared her hand and she's backed by state MP Alex Greenwich who on Wednesday told AAP the investment manager was "committed to action on climate change".
While Ms Heath, a director at Women for Election Australia, said she would be delighted to see a woman pre-selected for the Liberals, she added the community may be suspicious as to the party's motives.
"They're saying they weren't going to do it five days ago, now they are because of the numbers, not because they suddenly have a belief in all the benefits that a woman could bring," Ms Heath told AAP.
Mr Bragg, who AAP understands quit the pre-selection process in exchange for a safe spot on the Liberal Party's NSW Senate ticket, commissioned polling suggesting a woman would be better placed to win for the Liberals.
The polling revealed the Liberal primary vote has fallen to 39 per cent from 62 per cent when Mr Turnbull was the local member.
Woollahra councillor Mary-Lou Jarvis and Sydney East Business Chamber chair Katherine O'Regan now stand the best chance of being preselected when 210 Liberal members meet at Easts Rugby Union Club on Thursday.
Former Australian ambassador to Israel David Sharma is also in the mix.
Fellow candidate Carrington Brigham this week sent an email to some members asking them to vote on merit and not gender.
"If you believe I am the right person for the job, don't mark me down for my gender," Mr Brigham said in Tuesday's email.
City of Sydney councillor Kerryn Phelps is considering whether to stand as an independent, while Tim Murray is Labor's candidate.