A by-election for the Liberal safe seat will reportedly occur on October 6.

Mr Turnbull told his supporters at an electorate conference on Monday night that he would resign on Friday.

The move will leave the coalition one seat down for two sitting weeks, leaving new Prime Minister Scott Morrison in a precarious position with no majority in parliament.

Just days after Tony Abbott helped orchestrate Mr Turnbull's demise, he is now campaigning for his sister to replace him in his plum Sydney electorate.

Christine Forster on Monday confirmed she intends to run for Liberal pre-selection in Wentworth after being encouraged by several people within the party to replace the ousted prime minister.

Ms Forster also has the backing of her brother, who said she would be a good competitor in the impending by-election.

"She and I famously have had our differences but she is an outstanding individual," Mr Abbott told reporters in Sydney.

"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."

Mr Abbott was last week accused of being a "wrecker" by fellow Liberal MPs for laying the groundwork for the sudden move by the party's conservative wing against Mr Turnbull.

He had backed fellow conservative Peter Dutton who lost his chance at the top job when he was overtaken by Scott Morrison, who was sworn in as prime minister on Friday.

Ms Forster who is a City of Sydney councillor said she had a strong record of championing Liberal Party values at a local government level.

"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," Ms Forster told AAP.

"I've been strong in espousing and representing Liberal values in the city of Sydney."

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 GP Kerryn Phelps are also both considering running as independents.

Waverley Deputy Mayor Dominic Wy Kanak has been announced as the Greens candidate for the seat.

Tamarama Surf Lifesaving Club president and local businessman Tim Murray will run as Labor's candidate.

Australian Associated Press