Commissioner Heydon last week withdrew from delivering the Sir Garfield Barwick address over the possibility it could be described as a Liberal Party event.
But he says he was aware of the event's Liberal links as far back as April 2014, when he was first invited.
If the Australian Council of Trade Unions decides to apply for his removal over perceptions of bias, Commissioner Heydon will hear the application on Friday morning.
The situation is now one in which a Royal Commissioner will judge his own impartiality and fitness to continue in the position.
It comes as Mr Heydon admits to knowing of, and then forgetting about, Liberal Party ownership of a function he agreed to address later this month.
Mr Heydon says he advised the organisers he could only deliver the address if the Royal Commission had finished, which at that stage was due to be December 2014, but was extended by one year.
Mr Heydon says he had overlooked the Liberal connection when he received other emails about the event earlier this year.
"The email of the 10th of April did not state, and I did not understand from it, that the Sir Garfield Barwick address was in any sense a fundraiser for the Liberal Party. Email stated that it was organised by a body which I was told was 'one of the lawyer branches of the Liberal Party NSW division' which had a 'focus... On professional engagement'."
He withdrew from the event last week when he realised its Liberal party connections.
ACTU secretary Dave Oliver says lawyers need time to review emails indicating Mr Heydon knew as early as April 2014 the Liberal Party organised an event he was to address.
Mr Oliver says the unions say Commissioner Heydon might be perceived as biased.
"We have a genuine concern that he appears to be biased, and we would expect Commissioner Heydon to give the unions time to consider the evidence and time to determine what our next course of action should be. Now, in the meantime, once again, we are calling on Tony Abbott to shut down this political witch-hunt and stop wasting the taxpayers' money."
Labor's Treasury spokesman, Chris Bowen, says Mr Heydon's position is untenable.
Mr Bowen says he has no issue with Mr Heydon reviewing his own role as commissioner.
But he says there is genuine concern over perceptions of Mr Heydon's impartiality, and he's called on Mr Abbott to withdraw his commission.
"Dyson Heydon should should not be the Royal Commissioner. He's clearly fatally compromised as the Royal Commissioner and the Royal Commission needs to be not biased and and perceived to be not biased. Both of those tests have, in our view, been failed. Now there's a process though the Royal Commission that will unfold in coming days but Tony Abbott could show some leadership on this matter."
Prominent human rights lawyer Julian Burnside says Mr Heydon is an honourable man but he should stand down as Royal Commissioner.
Julian Burnside has told the ABC it would be possible to continue the Royal Commission into trade unions with another commissioner.
He says the issue with Mr Heydon is more political than legal.
"I think it's a pretty bad look to be as closely associated with the Liberal party as the circumstances suggest. I am sure there was no vice in his accepting the invitation but it was really never a tenable possibility for him to appear to be impartial on the Royal Commission while being so closely associated with the Liberal party as to accept that invitation."
The growing political storm comes as the Senate narrowly voted down for a second time a bill that would impose greater oversight on union officials.
The bill's second rejection came after independent senators Jacqui Lambie and Glenn Lazarus, and the Motoring Enthusiast party senator, Ricky Muir, sided with Labor and the Greens in blocking the amendments.
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