The Chief Justice will preside over a directions hearing for five members of federal parliament whose dual citizenship could disqualify them from their jobs.
Section 44 of the Australian Constitution prohibits dual nationals sitting in parliament.
Chief Justice Susan Kiefel will examine the cases of Coalition MPs Barnaby Joyce and Matt Canavan, One Nation's Malcolm Roberts and the Greens' Larissa Waters and Scott Ludlam.
Senators Fiona Nash and Nick Xenophon are expected to join the case later.
Commonwealth solicitor-general Stephen Donaghue asks in his initial submission to the court for the cases be heard together on September 13 and 14.
He has told the court Senators Nash and Xenophon, who have confirmed they are dual citizens of Britain, are likely to be referred when parliament sits again on September 4.
Independent senator Cory Bernardi says he believes the number of politicians caught out by the Section 44 provision could well increase beyond that group as well.
He says he will not believe assurances from fellow politicians about their citizenship status until he sees proof.
Senator Bernardi has told Sky News the Labor Party should be worried.
"I think Bill Shorten is in a spot of bother. He expects all of Labor to be taken at their word. But I don't believe anyone in this space, because I know at least one Member of Parliament who's not telling the truth."
News Limited is reporting more than 10 federal politicians potentially with dual nationality have refused to release documents proving they renounced their foreign allegiances.
Six of those are Labor MPs, three are from the Liberal Party, and one is from the National Party.
Opposition Leader Bill Shorten says he renounced his British citizenship in 2006 before nominating for the 2007 election but is refusing to release the official documentation to show it.
"The Constitution's very clear, and the Labor Party has clear screening processes. What I think is interesting is that the Government's saying they know they've got a problem and what they're instead doing is saying, 'Oh, question marks over Labor people, you've got to produce all your documentation.' I'm not interested in going down the path of feeding crazy conspiracies. Anyone who's going to the High Court, it's because they've actually recognised they have a problem and they know they have to go to the High Court, but, for the rest of the politicians, I don't think they have the same problems."
The Coalition's Christopher Pyne says Mr Shorten is making a strategic decision by not releasing proof of his citizenship status.
"Bill Shorten doesn't want to produce his documentation because he's worried that other Labor MPs would not be able to do so, so he's made the assessment they will simply shut down the shop and hope that the media will stop asking questions, because, if he releases his documentation, other MPs will have pressure to bear on them to release theirs -- like Penny Wong, for example. I notice that Anthony Albanese, he has released his birth certificate to The Australian newspaper to prove that he didn't have a father on his birth certificate, and, if it's good for Anthony Albanese, then it should be good for everybody else in the Labor Party who's in the same boat."
Anthony Albanese was raised by his mother, Maryanne Ellery, and his birth certificate only lists her.
The latest politician to face questions is Nationals MP George Christensen, born in 1978.
His mother arrived in Australia from Scotland.
Under changes to British laws in 2010, anyone born before 1983 with a British-born mother has been able to get British citizenship by registering.
Mr Christensen says he checked his citizenship status prior to entering parliament and checked again recently, confirming he was not a citizen of another country.
He says the advice from the British government via its online 'Check if you're a British citizen' page is that he does not have British citizenship.
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