Former prime minister Malcolm Turnbull has been lobbying his successor to have Peter Dutton referred to the High Court.
Mr Turnbull, who is holidaying in the US after stepping down last month during the Liberal leadership crisis, said Mr Dutton's constitutional position needs to be clarified.
"The point I have made to @ScottMorrisonMP and other colleagues is that given the uncertainty around Peter Dutton's eligibility, acknowledged by the Solicitor General, he should be referred to the High Court, as Barnaby was, to clarify the matter," he tweeted early Thursday morning.
Mr Dutton, whose leadership ambitions precipitated the events that led to Mr Turnbull's demise, has a family financial interest in two Brisbane childcare centres which receive Commonwealth funding.
At issue is whether this makes him ineligible to sit in parliament under section 44 of the constitution which disqualifies anyone who has a "direct or indirect pecuniary interest" in any agreement with the Commonwealth.
While advice was sought from Solicitor General during the leadership crisis, Solicitor General Stephen Donaghue could not categorically determine Mr Dutton's status, saying only the High Court could decide.
Mr Dutton has dismissed questions over his eligibility, saying Mr Donaghue's advice, and other "unequivocal" legal advice he has sought himself "puts to rest" any constitutional issues.
Section 44 of the constitution has tripped up several MPs over the past year including Barnaby Joyce, who was forced to recontest his seat after he was flushed out as a dual citizen.
One Nation leader Pauline Hanson said Mr Turnbull should cease his pursuit of Mr Dutton.
"I wish he'd just go and enjoy his life with Lucy," Senator Hanson told the Nine Network.
"He's had his go at running the country."
Meanwhile, Prime Minister Scott Morrison is checking whether Home Affairs Minister Mr Dutton stepped out of the cabinet when changes to child care funding were discussed.
Mr Dutton is also facing calls to withdraw a disparaging comment he made in parliament about former Australian Border Force boss Roman Quaedvlieg as part of a public spat over his intervention in at least two immigration cases.
The stoush between the two former Queensland police officers erupted over a disagreement over the chain of events that led to Mr Dutton's decision to grant visas to two au pairs held in immigration detention when Mr Quaedvlieg was head of the ABF.
Australian Associated Press