Tony Abbott's sister Christine Forster has confirmed her intention to nominate for Liberal preselection for former prime minister Malcolm Turnbull's seat of Wentworth in Sydney's east.
Mr Turnbull is yet to announce his resignation from the seat but told reporters last week it would be "not before too long".
The City of Sydney councillor said she had a strong record of championing Liberal Party values at a local government level.
In a statement to Fairfax Media, Cr Forster's spokesman said: "Christine can confirm her intention to nominate for preselection if and when the seat of Wentworth is vacated.
"But out of respect for Malcolm she won’t be commenting further until the former prime minister has made an announcement about his future."
Cr Forster said she had been encouraged by several people within the party to run for preselection.
"I think as someone with local credentials and a strong track record of strong liberalism, I feel they are the types of candidates we want in any seat," she told AAP.
"I've been strong in espousing and representing Liberal values in the City of Sydney."
Wentworth is one of Australia's wealthiest and most highly educated electorates.
Businessman and former Australian ambassador to Israel Dave Sharma is said to be the frontrunner to replace Mr Turnbull as the Liberal candidate.
NSW MP Alex Greenwich and health advocate Kerryn Phelps are both considering running as independents.
Dr Phelps, who is also a City of Sydney councillor, said she had not previously seriously considered going into federal politics but last week's leadership woes had created "exceptional circumstances".
"I've been very strongly encouraged by a lot of people to stand," she said.
"There is a lot of anger and despair over what has happened. I think a lot of people have had a gutful of party politics and politicking."
Dr Phelps was elected to the council as first on the ticket of Clover Moore's independent group, before she dramatically quit the team at a meeting last year.
She said speculation that she could be pitted against her council colleague Cr Forster was "putting the cart before the horse".
When asked how a tilt at the seat might affect her role on the council, Dr Phelps said any decision to nominate would require "a lot of considerations".
"I'm watching the situation very closely," she said.
Dr Phelps is a former president of the Australian Medical Association and works as a GP at a Double Bay medical practice.
While local councillors in NSW cannot serve as state members, there are no similar laws to prevent them serving as federal MPs.
Waverley deputy mayor Dominic Wy Kanak has been announced as the Greens candidate.
Tamarama Surf Lifesaving Club president and local businessman Tim Murray will run as Labor's candidate.
Support is also building for former acting Liberal Party director Andrew Bragg, a close friend and ally of Mr Turnbull, who ran the Coaltion's 2017 "Yes" campaign for the marriage equality vote.
Mr Turnbull's son-in-law James Brown has also been mentioned in the mix of potential candidates.
With AAP, Megan Gorrey and Lisa Visentin