A private member's bill, which would overturn the controversial "Andrews Bill" blocking both the ACT and Northern Territory from making its own laws on the issue, could be brought to a vote in the first half of 2018.

The senator who introduced it, Liberal Democrat David Leyonhjelm, said he was confident of it passing parliament, provided there was a conscience vote.

"I will require the support of the government to allow time for debate," he said.

"I am confident debate will resume and, provided there is a conscience vote, the bill will pass.

"I expect to bring on the vote in the first half of next year."

Currently, both Australian territories are unable to legislate euthanasia laws due to a bill introduced to parliament in 1995 by Liberal backbencher Kevin Andrews following the Northern Territory's decision to legalise euthanasia.

The Andrews Bill overturned the NT's decision two years later.

Senator Leyonhjelm told Fairfax Media he expects for debate on the issue to be reinvigorated after euthanasia laws passed Victoria's lower house two weeks ago.

The state's upper house began debating the bill this week, with a similar bill set to go before NSW's parliament later this year.

"My bill would not automatically make assisted suicide legal in the territories, but it would overturn the Andrews Bill and allow the parliaments of the territories to come to their own conclusions, like people in other states," Senator Leyonhjelm said.

"I have not encountered anyone from the ACT or NT who doesn't believe the Commonwealth should stop intruding into their decisions."

The senator first introduced his private member's bill in December 2015 and was set to be debated in 2016 but lapsed due to last year's federal election.

Following the bill's reintroduction in August last year, it was then debated on in February, with seven senators making speeches on the issue.

However, despite Senator Leyonhjelm's confidence of the bill passing, only 15 private member's bills introduced to parliament since 1901 have been passed into law.

The Liberal Democrat said it's in the interest of all parties to allow for a conscience vote.

"Like the issue of marriage equality, opinions on assisted dying are a matter of individual conscience," he said.

"While those in favour of assisted suicide will support me, I am also seeking the support of those who oppose assisted suicide but believe the territories should be free to debate and amend their own laws."

Despite the ACT having no legislative power to create its own euthanasia laws, attempts are also under way inside the Legislative Assembly to overturn the Andrews Bill.

Labor MLAs Tara Cheyne, Chris Steel and Michael Pettersson are petitioning the federal government to overturn the bill.

Ms Cheyne said the ACT should be allowed to make its own laws like other states in Australia.

"States right throughout Australia are actively debating voluntary assisted dying laws, but the ACT cannot due to outdated federal legislation made by people who don't represent us," she said.

Senator Leyonhjelm said state and territory governments should be able to come to their own decisions regarding legislation.

"The Commonwealth government should stick to its constitutionally prescribed role and not interfere in decisions that are the prerogative of the states and territories," he said.