The dual citizenship saga could threaten Malcolm Turnbull's knife-edge majority in parliament, with the Liberal Party checking the status of backbencher Julia Banks.
Melbourne-born Ms Banks has parents of Greek heritage but says she has never taken up Greek citizenship.
Her late father Phil Lolatgis migrated from Greece in 1949 as a 15-year-old, while her mother Helen was born in Australia.
"Both my parents were Australian citizens at the time of my birth," the MP for the Melbourne seat of Chisholm said in a text message on Friday.
"I have never taken up Greek citizenship."
However, it is understood that under Greek law she would have an entitlement to citizenship through her father - which could disqualify her as an MP.
Under the Australian constitution, a person is disqualified from being elected if at the time of their election they are a citizen of "a foreign power" or otherwise have an "allegiance, obedience or adherence to a foreign power".
A source with working knowledge of the Greek citizenship system said there was a "huge process" to go through, which involved registering the entire family in Greece and then registering individual children.
"It is not an automatic process," the source told AAP on Friday.
It is not known whether Mr Lolatgis, who died in 2007, took any steps in regard to Greek citizenship of his family.
Labor would have a strong chance of winning the seat of Chisholm in a by-election should Ms Banks be disqualified, ending the coalition's one-seat majority and forcing it into minority government negotiations with the crossbench.
She was first elected to the seat in 2016 by 2154 votes.
Questions have been raised about her citizenship status after LNP senator Matt Canavan resigned from cabinet upon discovering his mother had registered him as an Italian citizen without his consent. The issue will be tested in the High Court once the Senate refers the matter on August 8.
Greens senators Larissa Waters and Scott Ludlam both quit parliament after also finding out they held dual citizenship.
The government is considering asking the Senate to refer One Nation senator Malcolm Roberts to the court over questions about his UK links.
Australian Prime Minister Malcolm Turnbull being meet at a tram stop by Julia Banks in this file image. Source: AAP
"Obviously if we have a suspicion (about Senator Roberts), we'll check it up," Deputy Prime Minister Barnaby Joyce told reporters on Friday.
Senator Roberts was born in India in 1955 to a Welsh father and Australian mother and came to Australia in 1974.
On Thursday he told Sky News that when he filling out his candidate nomination form last year, he thought it best to double-check.
Senator Roberts wrote to UK authorities saying if they had him on the books he wanted to renounce his UK citizenship before election nominations closed.
They didn't confirm his correspondence until five months after he was elected.
If found ineligible, his Queensland seat would pass to the third person on the One Nation 2016 ticket, Fraser Anning.
However, Mr Anning is the subject of bankruptcy proceedings due to go to the Federal Court on August 22. Bankrupts are disqualified from being elected.
The fourth person on the ticket is One Nation Leader Pauline Hanson's sister, Judy Smith.