Three of the four senators replacing ousted dual citizens will be sworn in on Monday, but the eligibility of New South Wales Liberal Hollie Hughes to replace former deputy Nationals leader Fiona Nash is now under a constitutional cloud.

Key points: Section 44(4) of constitution bans people from holding parliamentary office if they also held an "office of profit under the crown"

Section 44(4) of constitution bans people from holding parliamentary office if they also held an "office of profit under the crown" Hughes was appointed to the Administrative Appeals Tribunal between losing the 2016 election and the Senate recount

Hughes was appointed to the Administrative Appeals Tribunal between losing the 2016 election and the Senate recount High Court to discuss the matter next Wednesday

High Court Justice Stephen Gageler said the Full Court should consider whether Ms Hughes has fallen foul of another section of the nation's founding document.

The Senate recount was ordered because Ms Nash was disqualified from the Upper House as she was a dual citizen at the time of the last election.

Ms Hughes was in an unwinnable position on the New South Wales Senate ticket, and missed out on election last July.

After that, she was appointed to the Administrative Appeals Tribunal (AAT) — the body which scrutinises government decisions.

While all the attention has been on section 44(1) of the constitution, and its ban on dual nationals sitting in parliament, there are concerns Ms Hughes may have breached section 44(4).

That section bans people from holding parliamentary office if they also held an "office of profit under the crown", effectively banning public servants from running for office while they are still employed.

Even though Ms Hughes resigned from the AAT before the Senate recount, her brief tenure at the tribunal could still breach that ban.

There are legal arguments that the court-ordered recount effectively means the election never ended, and Ms Hughes should not have taken a public service job.

The court will discuss the matter next Wednesday, the same day that the same-sex marriage survey result will be announced.

Concerns about Bartlett also mentioned

Justice Stephen Gageler has urged the lawyers to narrow their scope of arguments after reading an affidavit given to the court.

"It contains a great deal of hearsay material," he told the court.

"I do not believe we need to be burdened by that."

Concerns about the Greens' Senator-elect Andrew Bartlett because of the same issue were also mentioned.

Justice Gageler dismissed that, arguing no evidence had been presented to the court.

"I have no issue raised before me," he said.

Commonwealth Solicitor-General Stephen Donaghue QC told the court there had been some press reports about Mr Bartlett's position as a university lecturer.

But Justice Gageler said: "It's hearsay material."

"I see no reason why the order [allowing his appointment] should not be made," he said.

Not the first hurdle on Hughes' track to the Senate

Ms Hughes, a powerful member of the Liberal Party executive, missed out at last year's election after Malcolm Turnbull called a double-dissolution election — meaning all 12 Senate spots would be up for grabs — that saw her moved to the sixth spot on the shared Liberal-National ticket.

That effectively put her in an unwinnable position behind Defence Minister Marise Payne, Cabinet secretary Arthur Sinodinos, former senator Ms Nash, Liberal senator Concetta Fierravanti-Wells and Nationals senator John Williams.

At the time, she said she was "disappointed" and remained hopeful six senators could be elected.

Some Nationals had been hopeful Ms Hughes would take up Ms Nash's vacant Senate seat and then resign, creating a casual vacancy Ms Nash could step back in and fill.

The New South Wales Liberal Party is factionally divided and that split has already had an impact on Ms Hughes.