Interest in the constitutional monarchy brought Tony Abbott, Dyson Heydon and barrister Greg Burton together.
Royal commissioner Dyson Heydon and a Liberal Party member who invited him to speak at a dinner were both on a committee advising Tony Abbott on the move to a republic.
When Mr Abbott was executive director of Australians for a Constitutional Monarchy in 1993, Mr Heydon and barrister Greg Burton were appointed to a legal advisory committee to ACM.
Mr Burton is the NSW Liberal identity who invited Mr Heydon, now heading the unions royal commission, to address a party-organised event later this month.
Mr Heydon had agreed to deliver the Sir Garfield Barwick oration before last week declining because the event is also a fundraiser for the party.
The ACTU is considering whether to seek to have Mr Heydon disqualified from presiding over the inquiry because of perceived bias.
Unions have until Thursday afternoon to lodge a written application, and a hearing has been tentatively scheduled for Friday morning.
Mr Burton has also been mentioned as a possible Liberal candidate in the seat of Mackellar if former Speaker Bronwyn Bishop decides not to recontest it.
Mr Heydon was also on a panel which approved Mr Abbott's Rhodes scholarship when he was a Sydney University student in the early 1980s.