The Liberal vote in Malcolm Turnbull’s blue ribbon seat of Wentworth has nosedived since his removal as prime minister, new polling shows.

The research, commissioned by former Liberal pre-selection hopeful Andrew Bragg, found the party’s best chance to retain the eastern Sydney electorate was to stand a woman candidate.

Mr Bragg on Monday withdrew from the race, saying the party “should preselect a woman” when it meets to settle the pre-selection on Thursday.

According to the private polling, the Liberal’s primary vote has plummeted to 39 per cent, from 62 per cent when Mr Turnbull was the member.

Mr Turnbull held the seat for about 14 years and in the 2016 federal election he was returned with a massive two-party preferred count of 67.8 per cent of the vote.

The private polling also showed Labor’s Tim Murray was tracking with 25 per cent of the vote and Sydney City councillor Kerryn Phelps, who could run as an independent but is yet to declare her intentions, had 20 per cent.

Preselecting a woman candidate could lift the Liberal vote by four per cent, according to the polling published in The Australian, although this still implies the party will face a tough battle to retain Wentworth, which covers Sydney’s inner east all the way to Bondi Beach.

Prime Minister Scott Morrison said he’d like to see more women in federal parliament but it wasn’t up to him to preselect a candidate.

“We have not done as well in that area as I would’ve liked us to do but the party members are the ones who have to take on that responsibility,” he told Sydney’s 2GB radio on Tuesday.

Mr Bragg said his decision to drop out was influenced by allegations of bullying tactics used against women within the federal Liberal ranks made by outgoing Melbourne MP Julia Banks and former foreign affairs minister Julie Bishop, as well as broader concerns the party needs more women politicians.

“I believe these recent events and comments have changed the mood and accordingly I will withdraw my nomination,” Mr Bragg said in a Facebook post on Monday.

The Liberal preselection candidates for Wentworth include Woollahra councillor Mary-Lou Jarvis and Sydney East Business Chamber chair Katherine O’Regan.

Ms Jarvis, who is president of the NSW Liberal Women’s Council, was previously considered one of the biggest threats to Mr Bragg’s preselection chances.

But AAP understands senior Liberals in Canberra want Ms O’Regan to be the party’s candidate.

It is also understood Dave Sharma, a former ambassador to Israel between 2013 and 2017, remains interested in becoming the Liberal candidate.

Some 210 selectors from Wentworth branches will be involved in the Liberal preselection on Thursday evening.

The date for the by-election is still to be announced but it could be held next month.