Greens senator Andrew Bartlett could be referred to the High Court over whether the university job he held at the time of the 2016 election disqualifies him from parliament.
The Queensland senator was sworn in on Monday to replace Larissa Waters, who was found ineligible for parliament due to her dual citizenship.
The potential problems with his eligibility were discussed last Friday in another High Court case - regarding Liberal candidate Hollie Hughes - but the court still agreed to him being duly elected as no one brought a case against him.
Solicitor-General Stephen Donaghue told the court that did not mean the Senate could not refer Senator Bartlett to a hearing.
For many years there has been discussion about whether a university job could breach section 44 of the constitution, which disqualifies from parliament anyone who holds an office of profit under the Crown.
However it has never been tested in the High Court.
Liberal senator Eric Abetz said the Greens should refer Senator Bartlett to the court when parliament resumed on November 27.
If they didn't do so, the government should consider its own reference.
The court found in the Hughes case that her job as part-time member of the Administrative Appeals Tribunal disqualified her from replacing former minister Fiona Nash in the Senate.
However the reasons for the unanimous decision have not yet been published.
