The Greens and crossbenchers will seek to have all members of parliament lay their citizenship cards on the table.
The Senate will kick off a two-week sitting on Tuesday with a report by Senate President Stephen Parry.
The report will form the basis of a referral of stood-aside minister Matt Canavan to the High Court over his Italian citizenship.
Senator Canavan's mother registered him as an Italian resident abroad a decade ago, but he says this was done without his knowledge.
Under section 44 of the constitution, dual-citizens are ineligible for election to parliament.
The Greens will also refer ex-senators Larissa Waters and Scott Ludlam to the High Court, after they resigned over their Canadian and New Zealand citizenship respectively.
However, it remains unclear how One Nation will handle the matter of Queensland senator Malcolm Roberts, who was born in India and is believed to have held British citizenship which he says he has renounced.
The Greens will give notice of a motion on Tuesday in the lower house and Senate for an audit of all members of parliament, requiring them to produce documents proving they are not dual citizens.
The motion is not expected to be supported.
Greens senator Nick McKim believes it is the only way to get clarity on the issue.
Independent senator Derryn Hinch, who backs the audit, believes the major parties won't comply because they fear more of their MPs might be ruled ineligible.
Senator Hinch says he contacted Senator Roberts on the weekend and was keen to have a "little chat".
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.