Opposition Leader Peter Dutton is facing calls to allow his party room to have a free vote on supporting an Indigenous voice.
The Liberals will hold a party room meeting on Wednesday to discuss its position on the voice, after a proposal to alter the constitution was introduced to the parliament.
Liberal senator Andrew Bragg, who has previously indicated his support for the voice, wants the party to follow a precedent set by the republic and marriage equality debates, where MPs were not bound by one position.
Senator Bragg said historically the Liberal Party had not sought to bind its members to one view.
"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."
In an address to the National Press Club in Canberra on Monday, opposition spokesman for Indigenous Australians Julian Leeser questioned the proposed timing, urging Prime Minister Anthony Albanese to reconsider his plan to hold a referendum by the end of the year.
Senator Bragg said Mr Leeser had raised some important points which, if addressed, would lead to a successful referendum.
"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," the senator said.
"People don't want to see this referendum defeated."
A newly established Joint Select Committee on the Aboriginal and Torres Strait Islander Voice Referendum, made up of 13 members from the government, coalition and crossbench, is reviewing the bill and due to report by May 15.
Senator Bragg said the committee would make recommendations about the bill.
"(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," he 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."
