Communications Minister Mitch Fifield has confirmed Mr Parry told him he may fall foul of section 44 of the Constitution.
Section 44 disqualifies dual nationals from being elected to parliament.
"Former Senator Parry mentioned to me a few weeks ago that he was endeavouring to check his family's records," Senator Fifield said in statement to SBS News.
"The onus is on all senators and members to satisfy themselves of their circumstances and I encouraged Senator Parry to do so.
"He called me on Monday to say that he had sought advice from the British Home Office and had advised the Attorney General of this."
Mr Parry resigned from his position formally on Thursday after the UK Home Office confirmed he was a British citizen.
SBS News had earlier learned Mr Parry brought the issue up to a Cabinet minister back in August and was told to hold off on revealing his status.
A number of senior government officials have criticised Mr Parry for not disclosing his status sooner.
It's understood Mr Parry has been unhappy with reports that he failed to disclose his citizenship issues earlier.
Earlier, Prime Minister Malcolm Turnbull said he was "disappointed" Mr Parry did not speak out sooner.
"I learnt about it probably about the same time you did on Tuesday, yesterday," Mr Turnbull told reporters in Jerusalem on Wednesday.
"He chose to delay his reporting of it, he should have reported it much earlier and it could have been referred to the High Court together with the other matters that were dealt with, the other citizenship by descent cases."
Finance Minister Mathias Cormann and Liberal frontbencher Angus Taylor echoed similar sentiments.
Mr Taylor on Thursday said it “would have been better” if Mr Parry had come out earlier.
“He didn’t and it’s resolved now and we have to get on with it,” he added.
On Sunday, before Mr Parry’s dual citizenship status was revealed, Attorney-General George Brandis said he had no knowledge of any others inside the government who could have dual citizenship concerns.
Five politicians including former deputy prime minister Barnaby Joyce were ruled ineligible by the High Court after the court ruled ignorance of their dual citizenship status was not an excuse.
