While Scott Morrison's internal caucus rival for the last three years, Peter Dutton, is the heir-apparent for the Liberal leadership, the diminished moderates of the party want someone who can bring more women into the fold.
Simon Birmingham, the factional leader of the Liberal moderates and former finance minister under the Morrison government, was not prepared to say who he would be looking to take over the party leadership.
But whoever put their hand up needed to have a clear picture of how to rebuild the party in the areas it lost on Saturday, he said.
"And particularly how to ensure that we bring into the Liberal fold more Australian women and ensure they are preselected in far greater numbers so they we can ensure our party better reflects the reality of modern Australia within our rank," Senator Birmingham told Insiders.
The senator was keeping his options open on Mr Dutton's expected bid for the Liberal leadership role, saying the public's perception of the hawkish former defence minister's views were not always an accurate reflection of his true stance.
"It depends on who's willing to put their hand up and who's interested and then we can assess it from there ... I'll be talking to other some other colleagues too."
The Liberals were "paying the price" for not fully examining the loss of former prime minister Tony Abbott's seat of Warringah to Zali Steggall at the previous election, he said.
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He reflected on the soul searching the party would undertake on the loses to teal independents in blue-ribbon seats like Wentworth, Mackellar, North Sydney, Kooyong, Goldstein and Curtin.
"We should have acknowledged that had broader implications than just as it related to Tony," he said.
"You can go back to the same-sex marriage debate which dragged out unnecessarily long, but it should have been resolved by a simple conscience vote."
Another turning point was on climate reductions in the energy sector, he said, where the Liberal Party could have locked in a policy "and put some of these matters behind us" with a degree of bipartisanship on the National Energy Guarantee.
The failure to stand up for Liberal values and settle the climate wars earlier "has caused a significant price down the track."
The Liberal party needed to stand up for its values to win back voters who also hold those values, he said.
He deflected questions on the future of the Coalition agreement with the Nationals now they co-habit the opposition benches.
Barnaby Joyce was non-committal on recontesting the Nationals leadership on Sunday morning.
The Nationals retained all their seats, but both major parties lost seats to independents where so-called "captain's picks" were parachuted in without the backing of the local branches.
Some Liberal insiders have told ACM the former prime minister's pick of Katherine Deves in their attempt to win back Warringah played a significant role in the loss of the other blue-ribbon seats. Ms Deves became known for hateful comments about transgender people more than any other attribute or policy position.
Labor have all but lost the seat of Fowler with one of Labor's most prominent female frontbenchers, Kristina Keneally, falling short to independent Dai Le, after the party put her in as the candidate over the objections of local branches and the retiring Labor MP Chris Hayes.
The party isn't prepared to admit defeat just yet while counting is set to continue on Monday.
Labor deputy leader Richard Marles said the Ms Keneally had been an "enormous asset" for Labor in the Federal Parliament. As a former NSW premier and senator, she had been a fighter for the people of her state for the entirety of her political career, he said.
"She was very excited about representing the people of Fowler given the opportunity. We have not conceded it and whatever plays out there, we will work through the lessons of it."
Whether that was the end of Ms Keneally's political career was "too early" to say, Mr Marles said.