Senator Jane Hume has ruled out a tilt for the lower house, instead leaving the door open for a new candidate to fill outgoing Industrial Relations Minister Kelly O'Dwyer's shoes.
The senator is "very flattered and gratified" for the encouragement from within the party to run for preselection for Ms O'Dwyer's Melbourne seat of Higgins, but isn't ready to walk away from her work in the Senate.
"Everything I want to achieve I can do from the Senate," Senator Hume told ABC's Radio National on Monday.
"I did think long and hard about it, but I think the power of the Senate is greatly underestimated."
Ms O'Dwyer will quit politics at the next election to spend more time with her family and try for a third child.
Senator Hume hopes the minister's replacement is a woman.
"I do believe we need more women representing the coalition in parliament, but we want the best person," she said.
However, she says quotas are not the answer to help boost the numbers of women in the party.
"Liberal Party members do not like being told what to do. In our very nature we dislike that command and control, authoritarianism of the Labor Party," she said.
"That's why we feel uncomfortable with the idea of quotas as a solution."
If Ms O'Dwyer's successor fails to win at the next federal poll, the Liberals could be left without any Victorian women in the lower house since fellow Victorian Sarah Henderson's seat of Corangamite has become very marginal after a redistribution.
But Senator Hume says the party doesn't have a problem with women and has advanced their cause.
Although Ms O'Dwyer holds the blue-ribbon Higgins electorate by eight per cent, Senator Hume says the election contest will be an "uphill climb" due to a shift in sentiment.
Trade Minister Simon Birmingham also hopes his party's candidate for Higgins is a woman and, despite speculation, he believes it's unlikely former treasurer Peter Costello will try to win back his previous seat.
"I think it would be highly, highly unlikely and I suspect we will see new talent, fresh talent," he told ABC News Breakfast.
Queensland Labor MP Jim Chalmers says it's not a good sign of future Liberal candidates if Mr Costello is chosen to contest Higgins.
"It just shows how bereft they are of a pipeline of talent in the Liberal Party that they're considering going back some decades to bring back someone like Peter Costello," he told ABC's Radio National.
"That certainly would do nothing to fix the substantial problem the Liberal Party has with women."
Australian Associated Press