Designers of the Indigenous voice to parliament referendum hope a meeting with Opposition Leader Peter Dutton will help them clinch the support of the Liberal Party.

Prime Minister Anthony Albanese has also extended an olive branch to the Liberal leader, offering to come up with a constructive deal for constitutional reform in a private letter.

The letter, details of which were published in Nine newspapers, asked Mr Dutton for any “practical suggestions” he wished to contribute to the voice proposal.

“It is an extraordinary opportunity for every Australian to be counted and heard – to own this change and be proud of it,” Mr Albanese said of the referendum.

“As always, I am available to discuss these important issues with you in order to achieve a constructive outcome.”

The prime minister says the model and shape the voice will take will be decided by the parliament after the referendum, which instead focuses on enshrining the body in the constitution.

Indigenous Australians Minister Linda Burney has flagged that the voice may not come into place in this term of parliament, saying there’s no timeline on legislating the body if the referendum succeeds.

Ms Burney said while the “yes” campaign had more work to do ahead of the vote, it would be preferable for the Liberal Party to support the push.

“It would be extraordinarily wise and generous and in the spirit of what this referendum is going for, for that bipartisanship,” she told The Australian newspaper.

“But that is obviously going to be a decision of the Liberal Party.”

The Greens also remain split on support for the referendum after outspoken senator Lidia Thorpe said she would not support the voice without a guarantee that the constitutional chance didn’t cede Indigenous sovereignty.

Labor frontbencher Murray Watt said the government had advice supporting the sovereignty position and would be happy to provide the advice to Senator Thorpe.

Greens leader Adam Bandt said his party wanted to progress all elements of the Uluru Statement from the Heart, which includes treaty and truth-telling processes.

“We’ve been in discussions with the government now for some months and working through issues,” he told ABC TV.

“We’ve got the best opportunity for more than a decade, but potentially for a generation, of getting progress on First Nations justice.

“How can we ensure we get good progress on all of those elements?”

Mr Dutton will discuss the proposal of constitutional recognition with the government’s referendum working group on Thursday.

UNSW constitutional law professor Megan Davis, who is also the Uluru Dialogue co-chair, said she wanted to help clarify the mechanics of the voice and why it was important.

“Our hope is that Mr Dutton and his party room support First Nations peoples and help bring the whole country together to make this important constitutional change,” she said.

Bipartisan support has historically been needed for referendums to succeed.

The Nationals are opposed to the voice and Mr Dutton is weighing up whether the Liberals should also take a “no” stance or allow MPs a conscience vote.

– AAP