Prime Minister Malcolm Turnbull has described Scott Ludlam's oversight regarding his New Zealand citizenship as "remarkable".

Mr Ludlam, the Greens deputy leader, has stood down from the Senate after he was told he had not renounced his New Zealand citizenship, meaning he was ineligible to be a candidate for parliament.

"Obviously Senator Ludlam's oversight is a pretty remarkable one when you think about it - he's been in the Senate for so long," Mr Turnbull said.

"Anyway, there it is, he's ineligible, and so there'll have to be, I assume, a countback ordered by the High Court to produce a replacement for him."

Mr Turnbull was asked if Mr Ludlam would be required to pay back his salary.

"There is a practice about that, it'll be considered by the Minister for Finance is my recollection of the way it's dealt with in the past, so I'll leave that to be dealt with by him."

John Cameron, a Perth barrister, has admitted he informed the clerk of the Senate and then-senator, after he made the discovery.

Precedents for debt being waived

Sorry, this video has expired Greens senator Scott Ludlam resigns over failure to renounce dual citizenship

The Senate and the Department of Finance had pursued former South Australian Family First senator Bob Day and former West Australian One Nation senator Rod Culleton for repayment of salaries and allowances.

The Federal Government later agreed to waive debts owed by Mr Day, who the High Court had ruled was not validly elected.

Former WA senator Rod Culleton was asked to pay back his salaries and allowances. ( ABC News: David Weber )

The government said it had advice Mr Day may have been unable to repay the funds.

In May, Deputy Prime Minister Barnaby Joyce said Mr Culleton had received the same letter as Mr Day outlining options related to the debts.

The ABC's election analyst Antony Green said he thought it was unlikely Mr Ludlam's salary would be clawed back.

"In the past, the rule has been that they've waived that, Senator Ludlam has worked as a senator, carried out the functions, done constituency work, he's attended parliament, so he's done all the work," said Green.

"The question of qualifications has come up — the parliament doesn't usually try and get the salary back.

"It's history making, there's three senators have now been ruled out all by different sections, different parts of section 44 of the constitution — we've had a disqualification for a conviction, one for a conflict of interest, and now one for citizenship."