The High Court has the "power and duty" to hear a challenge against Assistant Health Minister David Gillespie's eligibility to remain in federal Parliament, according to the Labor candidate he defeated at the last election.

Peter Alley wants the High Court to consider whether Dr Gillespie's financial interests breach the constitution, and his lawyers have argued the current citizenship crisis only serves to bolster their arguments.

The Nationals MP owns a shopping centre in Port Macquarie on the New South Wales mid-north coast.

One of his tenants is an Australia Post franchise.

While all the recent attention on the eligibility of politicians has been on the citizenship crisis, Mr Alley is arguing Dr Gillespie is in breach of another part of the constitution which bans federal politicians benefitting financially from the Commonwealth.

Earlier this year, the High Court ruled former South Australian senator Bob Day was ineligible to hold office because of an indirect financial interest in a property leased to the Commonwealth, that he used for his electorate office.

The avenue for Mr Alley to bring that case is tricky, because he first needs to prove he has sufficient interest in the case to get the High Court to consider the matter.

The usual process is for Parliament to formally refer questions over a member's eligibility to the court.

The Commonwealth, unsurprisingly, has argued the court should not hear Mr Alley's challenge.

But Mr Alley's lawyer, Bret Walker SC, has told the court it "has both power and duty to do so".

"The duty is somewhat heightened in circumstances where there is a clearly arguable case... where there has not been a referral from the House and where there has been nine recent referrals in relation to other purported parliamentarians," Mr Walker told the court in written submissions.

He argued waiting for the House of Representatives to formally refer questions on Dr Gillespie's eligibility to the High Court was relying on "political will".

Mr Walker recently represented former deputy prime minister Barnaby Joyce and former deputy Nationals leader Fiona Nash in their unsuccessful citizenship cases before the High Court.

The High Court will next hear the case on December 12.