Labor MP Susan Lamb is hanging onto her seat despite questions about her British citizenship, but the government believes a referral to the High Court is "irresistible".
The Longman MP is a British citizen by descent but the UK Home Office could not process her renunciation before the 2016 election because it could not be satisfied from the documents available that she held British citizenship.
Attorney-General Christian Porter said Opposition Leader Bill Shorten should send Ms Lamb's case to be tested in the High Court.
"I think it's almost to the point now where it's irresistible the argument that (Mr Shorten) should refer and my view is he likely will in the very near future," he told Sky News on Monday.
Manager of opposition business Tony Burke says Ms Lamb has clearly taken every reasonable step she can to renounce UK citizenship.
But he said Liberal MP Jason Falinski had taken no steps to relinquish his Polish citizenship.
Labor wants all MPs potentially breaching Section 44's ban on dual citizenship to be referred to the High Court.
"Let's just refer them all, and it's done," Mr Burke told ABC radio.
Prime Minister Malcolm Turnbull said Mr Shorten was standing up for the rights of British citizens to sit in Australia's parliament, with Labor MP David Feeney taking months to resign.
"It took months and months to get the then-member for Batman to resign and the member for Longman is still hanging in there," Mr Turnbull told parliament.
"It may well be in the leader of the opposition's mind there will always be an England, but there will always be a section 44 as well."
Leader of the House Christopher Pyne said the government would refer Ms Lamb to the High Court if Labor refused to.
"We'd rather not refer people unilaterally," Mr Pyne told ABC radio.
Greens leader Richard Di Natale said the saga could have been resolved when the Greens proposed an audit to put the issue to bed.
Ms Lamb argues she took all reasonable steps to renounce her citizenship in time to run for the July 2016 federal election.
But authorities told her in a letter in August 2016 they could not process her renunciation.
