His claim came as Prime Minister Malcolm Turnbull criticised Senate President Stephen Parry after he resigned because of his dual citizenship.
Senior Liberals are confident there will be no more citizenship surprises in the party after the dramatic resignation of Tasmanian senator Stephen Parry.
As the Liberals continued to dismiss calls for an audit of parliamentarians' citizenship, the Immigration Minister claimed former Prime Ministers could've been in breach of section 44 of the constitution.
"I suspect if you go back over last decades, you'd find people, including prime ministers frankly, who weren't qualified," Minister Dutton told Nine's Today on Thursday.
"But the onus is on the individual to demonstrate they're eligible, they're in compliance with that particular provision of the constitution."
Malcolm Turnbull says he's disappointed Stephen Parry didn't disclose his dual citizenship and potential ineligibility to sit in parliament earlier.
"I'm disappointed Senator Parry didn't make public this issue quite some time ago. I learnt about it the same time as you did, on Tuesday," he told reporters in Jerusalem on Wednesday.
Finance Minister Mathias Cormann agreed the outgoing senator should have acted sooner.
Senator Parry confirmed on Wednesday he was a dual Australian-British citizen. His father was born in the UK.
The bombshell followed a High Court ruling that found five Australian politicians, including former deputy prime minister Barnaby Joyce, were ineligible to sit in parliament because they held dual-citizenship.
"[Senator Parry] should have acted sooner, there is no question about that," Mr Cormann told ABC's 7:30.
But Prime Minister Turnbull turned down calls to conduct an independent audit into the status of all federal politicians, saying every parliamentarian had an obligation to ensure they did not breach the Constitution.
"What is an audit?" he asked reporters.
"Does that mean that somebody is going to undertake extensive genealogical research on every member of Parliament and senator? Undertake extensive research into foreign laws?"
Mr Cormann was pressed by ABC presenter Leigh Sales on Wednesday night about whether the government would conduct an audit given Mr Parry had stalled his self-investigation.
The Finance Minister argued such a mechanism would lead to "less certainty".
"We need to be very careful about the consequences that would come from this [an audit]," he said.
"In the context of actually wanting to ensure that people can have confidence in the parliament, in the compliance of members of parliament with the Constitution, the most appropriate body to assess and adjudicate over any issues if and as they emerge is the High Court.
"Only the High Court can deliver a conclusive resolution in relation to any issues."
The court found five politicians were ineligible including Mr Joyce, The Nationals' Fiona Nash, former Greens senators Larissa Water and Scott Ludlam, and One Nation's Malcolm Roberts.
Two others – Nationals' Matt Canavan and Nick Xenophon of the Nick Xenophon Team – were ruled eligible.
Section 44 of Australia's Constitution mandates candidates to the Parliament of Australia must not be a citizen or "entitled to the rights or privileges of a subject or citizen" of a foreign power.
Mr Joyce joined in the criticism of his Coalition colleague, Senator Parry, for not revealing he could be a dual-citizen as soon as he had doubts about his eligibility to sit in parliament.
"All I can say is the National Party, when we had doubts, we owned up straight away and went to the High Court," he told AAP just hours before Senator Parry confirmed he was a British citizen and was resigning.
"I think it's incumbent upon all people in parliament that have concerns, that they're to state them."
Opposition leader Bill Shorten blamed Malcolm Turnbull for the state of the Australian parliament.
"Because of his arrogance and his poor judgment, we've now got the current turmoil," Mr Shorten told reporters in Jerusalem on Sunday night.
With AAP
