Independent MP Andrew Wilkie has queried the prime minister’s plan for a citizenship register through which federal parliamentarians will publicly detail their citizenship history.

“Regrettably I don’t have confidence in all members and senators to be fully open and transparent and honest,” Wilkie told ABC radio on Tuesday.

Turnbull said the reality was that MPs would be required to state where their parents were born and the date of their birth.

“That’s something that is pretty hard to conceal, you know?” he said.

The system of voluntary disclosure with political, personal and reputational penalties would work well, the prime minister insisted.

Turnbull wouldn’t buy into the possibility he might lose another MP after Liberal backbencher John Alexander revealed he may be a British citizen by descent.

“I’m not going to start front-running process,” he said.

Alexander is seeking urgent advice on whether he is a UK citizen through his British-born father Gilbert Alexander who was born in England in 1907 and arrived in Australia in 1911.

A search of British records found no trace of Gilbert Alexander, who died in 1987, having formally renounced his UK citizenship before his son was born in 1951.

Alexander believes he’s in the clear.

“(My father) became an Australian citizen as soon as he could. I understand he renounced his British citizenship before I was born, because he was a proud Australian,” he said.

“I was born in 1951 as an Australian citizen.”

Assistant Minister Craig Laundy is concerned foreign citizenship has been demonised, and wants the government to consider constitutional changes to allow dual nationals to run for parliament.

“Whether it’s a referendum, whether it’s something else, we need to work out a way where we can make it happen,” Mr Laundy, who holds an ethnically diverse marginal Sydney seat of Reid, told ABC radio on Tuesday.

“I just don’t think it should be a reason you should be disqualified from standing for parliament.”

Cabinet minister Mathias Cormann does not believe the citizenship purge will cost the Coalition government power.

“But obviously this is a matter of making sure the Australian public can have full confidence in the integrity of the parliament,” he told ABC radio.

“The steps the prime minister has laid out yesterday will ensure that happens.”

Cormann did not reject Laundy’s idea outright, saying a parliamentary committee was investigating how the issue could be better dealt with in the future.

If Alexander is disqualified from parliament, the government would be forced to a by-election in Bennelong which the MP holds with a 7.8 per cent margin.

– AAP