MALCOLM Turnbull says he will resign from Parliament on Friday after what he called a "pointless week of madness."

The Prime Minister's exit could trigger an October 6 by-election in his Sydney seat of Wentworth and potentially cost the Government its one-seat majority.

Mr Turnbull will write to constituents tomorrow to explain why he is leaving.

"My prime ministership has come to an end. The circumstances have appalled most Australians but again, I won't labour the point," he told a gathering in his electorate on Monday night, Fairfax reported.

"I don't want to dwell on the shocking and shameful events of the last week, a pointless week of madness that disgraced our parliament and appalled our nation."

He thanked his supporters, adding: "Former prime ministers are best out of Parliament, not in it, and I think recent events best underline the value of that observation."

Liberal candidates will have less than a week to put their names forward for the seat of Wentworth, with several including Tony Abbott's sister Christine Forster already throwing their hats in the ring.

"I have decided today I will nominate because a lot of people inside the party are encouraging me to do so," Ms Forster told The Australian.

"It's a difficult situation and I don't want to be seen to be disrespecting Malcolm - who I do respect," Ms Forster told AAP.

Mr Abbott said his sister would be a good competitor in the impending by-election.

"She and I famously have had our differences but she is an outstanding individual," he told reporters in Sydney just days after helping to orchestrate Mr Turnbull's demise.

"If she does put her hand up for Wentworth and if she is successful, I know she will be a wonderful, wonderful competitor in any by-election and she'd be a great local member if she were elected."

NSW MP Alex Greenwich and GP GP Kerryn Phelps were considering running as independents in the eastern suburbs seat.

"A good community-based independent could win," Mr Greenwich said in a statement on Friday. "We do well at state and local elections."

David Sharma, a former ambassador to Israel between 2013 and 2017 who works in government affairs, is said to be one of the frontrunners.

Mr Turnbull's son-in-law, former army officer James Brown, ruled out the possibility of standing.

Waverley Deputy Mayor Dominic Wy Kanak has been announced as the Greens candidate for the seat and Tamarama Surf Lifesaving Club president and local businessman Tim Murray will run as Labor candidate.

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