The former prime minister has told supporters he will quit as the member for Wentworth on Friday, with a by-election tipped in October.

Liberals are lining up to replace him in the blue ribbon eastern Sydney seat, with Tony Abbott's sister Christine Forster among those putting her name forward.

Mr Joyce, a former Nationals leader, quit as Mr Turnbull's deputy following an affair with a staff member who had his child.

The backbencher argued it would be "more honourable" for Mr Turnbull to serve out his term on the back bench alongside him.

"You leave on the right terms with the electorate and the right terms with your nation," Mr Joyce told Seven Network.

"To say 'oh well I'm not the prime minister anymore ho hum, you guys might lose government' - the government that he led - I think people are really disappointed with him about that."

Business Council of Australia executive director Andrew Bragg resigned his post on Tuesday morning to run for preselection in Wentworth.

"I thank Jennifer Westacott, the staff and members for the opportunity. Under the party's rules, I am unable to make further comment on the preselection," he posted to social media.

Dave Sharma, Australia's former ambassador to Israel, has also entered the race.

Mr Abbott, who helped orchestrate Mr Turnbull's demise, endorsed his sister to replace his arch-nemesis.

Ms Forster, 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," she told AAP.

Mr Turnbull comfortably held the blue-ribbon seat of Wentworth with a margin of 17.7 per cent at the 2016 election.

Labor's candidate for the seat, local businessman Tim Murray, has earned praise from a potentially surprising source - Mr Turnbull's Singapore-based son.

"He's a great guy and I know him well," Alex Turnbull told Fairfax.

Independent Tasmanian MP Andrew Wilkie believes a decent unaligned candidate could snatch the seat.

"It is ripe for a really high-profile independent to pick up the disaffected Liberal voters and also the more progressive voters," Mr Wilkie said.

NSW independent MP Alex Greenwich has confirmed he will not run as an independent in the seat, while GP Kerryn Phelps is still considered a tilt.

Australian Associated Press