Keenan tweeted on Thursday morning that he did not hold citizenship of any country other than Australia.
However, he has not produced any paperwork and he and senior ministerial colleagues, Scott Morrison and Peter Dutton, are resisting calls for him to do so.
The Justice Minister's name is the latest to be linked to the section 44 saga, which has also ensnared Deputy Prime Minister Barnaby Joyce, Greens MPs Larissa Waters and Scott Ludlam, Liberal Matt Canavan and One Nation's Malcolm Roberts.
Joyce, the second most senior politician in Australia, has had to renounce New Zealand citizenship, but the High Court is still to determine whether there is a breach of the Constitution, disqualifying him from holding office.
1/3 I am an Australian citizen and I do not hold citizenship of
any other country. Fairfax is aware of this, yet in a cheap grab #auspol
— Michael Keenan MP (@MichaelKeenanMP) August 16, 2017
Fairfax media, which originally reported the story, said it had contacted Keenan's office repeatedly to only be told Keenan was an "Australian citizen".
Treasurer Scott Morrison told reporters in Canberra the Minister's tweets were enough, "I think Michael's dealt with the matter this morning. He actually dealt with it a long time ago."
UK consultancy firm and immigration experts Sable International was quoted by Fairfax as saying that because Keenan's father was born in the UK, he would have received British nationality "by descent".
Additionally, he would not have been required to renounce this British citizenship to be an Australian citizen.
Keenan said he formally renounced his UK citizenship in 2004, before entering parliament.