Coalition MPs are now openly voicing concern the citizenship saga that has been gripping Canberra is damaging the Federal Government.

Key points: Liberals urged to back citizenship audit of every politician

Liberals urged to back citizenship audit of every politician Cory Bernadi says claims another MP privately admits they aren't eligible

Cory Bernadi says claims another MP privately admits they aren't eligible Bill Shorten labelled a hypocrite for not releasing citizenship documents

With fresh questions about the eligibility of different MPs and senators emerging almost every day, Liberal backbencher Craig Kelly believes there is a solution to the chaos, backing the Greens' push for an audit of the citizenship status of every politician.

It is a bold move, given his own party has rejected the idea.

However, Mr Kelly said the issue had been damaging the Coalition for too long.

"The reality is where there's a bit of confusion around in the media about what's actually happening with the High Court decision, it reflects in the Government's polling," he said.

"So, it's in our best interests to clear this issue up as quickly as we possibly can and get on with issues that are important to Australians."

Greens leader Richard Di Natale is urging other Liberals to back the audit.

"It's very clear there are individuals who privately support an audit and now we've heard some of those people step forward and publicly support what the Greens have been saying since this whole mess started," he said.

"But what we need to do is see more of them express their views and hopefully the Prime Minister will see reason."

The constitution prevents anyone with dual citizenship from holding office, and there are now seven MPs and senators who have been referred to the High Court to see whether they can remain in Parliament.

A preliminary hearing is scheduled for Thursday, however Attorney-General George Brandis said he does not think there will be an outcome until October.

Mr Kelly wants the audit to come after the High Court rules, however crossbencher Cory Bernardi is eager for immediate action.

"Now it's up to the leadership of the Liberal Party and the Government to say we need to have a full audit of all MPs and senators, we need to make sure the integrity of the parliament is crystal clear, until the High Court makes its judgment the parliament needs to be prorogued."

Senator Bernadi repeated claims there is at least one MP who is not eligible to sit in parliament.

"One of my colleagues — a Member of Parliament — publicly said they are completely eligible under Section 44 to be in parliament, yet privately have admitted, and their staff have admitted, that they're not eligible," he said.

"Important legislation could be passed on the strength of someone's vote whom is not entitled to be there by their own admission."

Shorten a hypocrite, Coalition MPs say

Coalition MPs fear the beneficiary of the citizenship uncertainty is the Opposition Leader Bill Shorten, and some in the Coalition have decided it is time to turn the citizenship blowtorch on him.

Mr Shorten claims he renounced his UK citizenship in 2006, but the Coalition wants to see proof.

The Assistant Minister for Cities, Angus Taylor, told Sky News yesterday the Opposition Leader was being a hypocrite because he was refusing to show documentation he rescinded his British citizenship.

Mr Kelly also accused him of hypocrisy.

"We had the Opposition Leader Mr Shorten saying today that he believes he has no issues with citizenship, but when he was asked to show some documentation to prove it — he's refused to show it," he said.

"You can't have it both ways, members of the Labor Party can't be out there accusing members of the Coalition, but when they're asked to show some documentation about proof they are not ineligible under section 44 they refuse to show any documents."

On the ABC's Q&A program last night, host Tony Jones repeatedly asked Mr Shorten if he would release his citizenship paperwork.

Sorry, this video has expired Bill Shorten says he won't hand over papers proving he's not a British citizen

But Mr Shorten insisted Labor's vetting process was sufficient.

"Just because a Liberal makes an accusation doesn't mean the rest of us have to put our hands up and start going through the filing cabinets," he said.

"Some people are never going to be satisfied."