The party's recently appointed president Tony Abbott, a former Liberal prime minister, has personally phoned members of NSW branches to try to stop them leaving, according to The Sunday Telegraph.
Pauline Hanson's party is now the most popular in Australia, leading both Labor and the coalition on primary votes, according to multiple opinion polls.
Asked about Mr Abbott's bid to quell members' concerns, Mr Taylor said he understood their sense of frustration.
"They want a better Liberal Party and, particularly in NSW, we have seen a number of members of the party frustrated at the lack of democracy in the party," he told Sky News on Sunday.
"I've been fighting to change that for many, many years, and I will continue to, and I want those people to stay.
"Tony, as president, is doing a great job at getting out and energising the membership, retaining those who are frustrated."
Mr Taylor, who successfully ousted Sussan Ley as Liberal leader in February, said the party had a "credible plan" and would focus on bringing new people in.
The coalition has already lost members of its ranks to One Nation, including former South Australian Liberal senator Hollie Hughes and one-time Nationals leader Barnaby Joyce.
One Nation has also reported a growing membership base and claims its "fire the liar" fundraiser, aimed at removing Prime Minister Anthony Albanese, has brought in more than $4.75 million in donations from some 76,000 people.
The fundraising drive was in response to Labor's call for members to donate $27 for a social media campaign targeting One Nation.
Labor is trying to position the right-wing party as one of grievance rather than a legitimate alternative government that offers solutions.
The Liberal Party hasn't ruled out preferencing One Nation over Labor at the next federal election.
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