Senate crossbenchers want foreign-born politicians to prove they revoked their citizenship of another country before standing for parliament.
Independent senator Derryn Hinch, who with the Greens is leading the charge for an independent audit, believes the major parties won't comply because they fear more of their MPs might be ruled ineligible.
The issue will be discussed at a meeting of crossbenchers on Tuesday.
Senator Hinch says he contacted One Nation's Malcolm Roberts on the weekend about the Indian-born senator's right to sit in parliament.
"So we'll have a little chat," Senator Hinch told reporters in Canberra.
Greens senator Nick McKim says an independent audit by a person appointed by a parliamentary committee would allow every MP to provide proof of their citizenship status.
The minor party has lost two of its senators - Scott Ludlam and Larissa Waters - after both revealed they had been ineligible to stand for parliament because they held dual citizenship.
Nationals senator Matt Canavan also has stood down from cabinet over dual citizenship his mother obtained for him from Italian authorities.
The Senate is expected to refer his case and that of Senator Roberts to the High Court for a ruling.
Labor does not see any need for an independent audit.
"It's a matter for every person who stands for election to this parliament to be aware of the requirements of the Constitution," shadow attorney-general Mark Dreyfus told reporters.
Labor senator Doug Cameron accused the Greens and One Nation of acting unprofessionally by failing to ensure the citizenship status of their candidates.
"I think it's a bit of a stunt," he said.
The British-born senator says the ALP secretariat always ensures the eligibility of its candidates.
"I know I'm eligible and was eligible when I stood. And that's because I'm a member of a professional party," he said.