Tony Abbott’s sister Christine Forster wants to be the Liberal candidate in Malcolm Turnbull’s soon-to-be-vacated Sydney seat as several big names jostle for the plum position.

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

Turnbull is yet to announce his resignation from the harbourside seat but told reporters last week it won’t be long.

“It’s a difficult situation and I don’t want to be seen to be disrespecting Malcolm – who I do respect,” Forster said on Monday.

The City of Sydney councillor, a vocal advocate of same-sex marriage during last year’s postal survey, 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,” Forster said.

“I’ve been strong in espousing and representing Liberal values in the city of Sydney.”

Abbott said on Monday that his sister would make a great MP.

“If she is successful I know she would be a wonderful competitor in a byelection, and she’d be a great local member if elected,” the former prime minister said at a function in Sydney.

But as Guardian Australia reported on Friday, businessman and former Australian ambassador to Israel Dave Sharma is said to be the frontrunner to replace Turnbull as the Liberal candidate. Sharma formerly worked for Alexander Downer as a legal adviser and is understood to have the backing of the Liberals’ moderate faction, which controls the majority of Wentworth branches.

Turnbull’s son-in-law, James Brown, a non-resident fellow at the University of Sydney’s US Studies Centre, was touted as a possible Liberal candidate, but ruled it out on Monday.

In a tweet thread Brown said he had “a young family to look after and a mission to complete” at the RSL New South Wales, of which he is president.

Serving in the Australian parliament would be an enormous honour but whenever @turnbullmalcom resigns I will not be standing for preselection in Wentworth. Thanks to those who have kindly suggested I should. I have a young family to look after and mission to complete @RSLNSW — James Brown (@captainbrown) August 27, 2018

Tamarama Surf Lifesaving Club president and local businessman Tim Murray, an economist and commodities expert who spent 20 years living in China, will run as Labor’s candidate.

NSW MP Alex Greenwich and health advocate Dr Kerryn Phelps – both veterans of the successful marriage equality campaign – are being urged to run as independents.

Greenwich told Guardian Australia he is sticking with his job in the state parliament.

“I hope a good community-based independent comes forward ... the Morrison government would not reflect the views of the seat of Wentworth,” he said.

Phelps said she had been “very encouraged by the messages of support from people in Wentworth who would like me to stand when an election is called”, but she noted Turnbull was yet to formally resign.

The Waverley deputy mayor Dominic Wy Kanak has been announced as the Greens candidate for the seat.