Senator Andrew Bragg has called for the Liberal party room to have a conscience vote on supporting the Indigenous Voice to Parliament referendum.
Senator Bragg referred to previous debates within the Liberal Party where MPs were not limited to voting for a particular position.
"In the past you've had (former prime minister) John Howard voting 'no' on the republic and (former treasurer) Peter Costello voting 'yes'," he told ABC Radio National.
"Then you had (former prime minister) Malcolm Turnbull voting 'yes' on marriage equality and other members of his cabinet voting 'no'.
"That has always been part of the Liberal tradition, so that is my starting point."
Senator Bragg's comments follow opposition spokesperson Julian Leeser's National Press Club address on Monday, where he urged Prime Minister Anthony Albanese to reconsider holding the referendum by year's end.
The New South Wales senator, who has previously indicated his support for the Voice, said Mr Leeser raised some valid points which needed addressing for the referendum to be successful.
"This idea should sell itself, it's a very good idea, and I feel that it has incurred a lot of brand damage because of the way that the process has run," he said.
"People don't want to see this referendum defeated."
The recently established Joint Select Committee on the Aboriginal and Torres Strait Islander Voice Referendum is currently reviewing the constitutional amendment bill following its introduction to parliament last week, with a report due back by 15 May.
"(The committee) can now look at the wording, but it can also look to generate some positivity about the benefit of new institutions to support Indigenous people in our country," Senator Bragg said.
"This is a vote of the Australian people, it's not a vote for politicians.
"Our job is to give advice to people if they are wanting to hear from us about how they should vote for the upcoming referendum."
The Liberal Party will hold a meeting Wednesday to discuss the federal party's position on the Voice.
