Tasmanian Liberal Bridget Archer could put her hand up as deputy leader to keep the party from moving further to the right, amid speculation Peter Dutton will become leader.
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But her colleague Tasmanian senator Eric Abetz says a move to the left is what cost the Liberals the federal election.
Ms Archer, first elected in 2019 and expected to retain her ultra marginal seat of Bass, said she backed traditional "Liberal values".
Asked if she would consider a tilt at the deputy spot, given the risk the party could move further to the right with Mr Dutton at the helm, she said "potentially".
"I've seen some early commentary around some idea that the party should move further to the right and I will certainly resist all efforts for that to occur," she told ABC radio on Monday.
"We need to bring the party back to the centre."
Former Communications Minister Paul Fletcher would not be drawn on who he would support as the next leader of the Liberal party, or his own aspirations.
"We don't even yet know the final composition of the party room. We haven't seen who's putting themselves forward," he told the ABC on Monday.
"I'm confident that we'll have a strong leader, strong deputy leader. My aspiration will be to continue to serve as part of an effective team as opposition."
Mr Fletcher said female voters had shown issues which affected them would need to be addressed.
"There's also a clear message there about having a strong focus as a Liberal Party on measures to ensure that women have equality of opportunity, equality of outcome in the workforce and in many other aspects of life," he said.
Yet Senator Abetz said the Liberal Party's move to the left was its undoing at the ballot box.
"It was the so-called, self-styled 'modern Liberals' that the electorate dealt with relatively harshly," he told ABC Hobart radio.
"There's no doubt that Peter Dutton has the strength and leadership skills to be a very effective opposition leader ... I know what the media will say, he's unelectable."
In relation to the deputy leader position, Senator Abetz said it was too early for Ms Archer to be considered.
Mr Dutton is widely expected to become the opposition leader although other names have been floated, including ex-home affairs minister and Queenslander Karen Andrews and former trade minister and Victorian Dan Tehan.
Former environment minister Sussan Ley has been floated as a potential deputy leader.
Ms Andrews said she was considering which role in the party she could best contribute to before the Liberals meet to decide on the leadership.
"I'm going to consider my position over the next day or so ... I want to really consider which role I feel I am best able to add the most value," she told Brisbane radio station 4BC.
Liberal senator James Paterson said Peter Dutton was the right choice to lead the party and there was a consensus forming around him as "the right choice for these times".
Queensland MP Stuart Robert rejected suggestions Mr Dutton, the former defence minister, could take the Liberal party further to the right.
"The key thing for the Liberal-Nationals parties is to represent aspiration," he told Nine Network.
"We have always been a sensible centre-right party and that is where we should stay."
Mr Robert also addressed the Liberal party's "woman problem" in the wake of an almost all-female slate of independents winning their seats and knocking off mainly moderate Liberal MPs.
"Everything is on the table ... to ensure that we can properly represent every single part of Australia," he said.
Ex-prime minister Scott Morrison will formally step down from the Liberal leadership when the top job is spilled at the next party room meeting.
The latest official figures have the coalition holding 58 lower house seats in the new parliament.
Australian Associated Press
