Prime Minister Tony Abbott has declined to say whether the government had begun canvassing for a new royal commission chief to replace Dyson Heydon, but has insisted the inquiry "will go on".

Mr Abbott refused to weigh in on Thursday whether Mr Heydon should step down as the head of the royal commission into trade unions ahead of a decision the retired High Court judge is due to make on his fate on Friday.

Mr Heydon will announce whether he will resign from the royal commission due to an appearance of bias after Fairfax Media revealed two weeks ago he was to be the guest speaker at a Liberal Party fundraiser.

Both Mr Abbott and Opposition Leader Bill Shorten have said the commission can continue under another commissioner if Mr Heydon steps down.

"The important thing is that the royal commission will continue," Mr Abbott said.

"We have seen an abundance of evidence of rorts, rackets and rip-offs inside the union movement.

"This is an absolutely vital royal commission, even someone of the stature of Martin Ferguson says this is an important part of cleaning up the union movement, cleaning up the Labor Party so it must and will go on regardless of any decision Dyson Heydon QC makes."

Mr Abbott said he would not pre-empt Mr Heydon's decision by giving his view on whether he should continue in the role.

"I'm not going to pre-empt the decision that he as the royal commissioner has to make other than to say he is a man of the most profound integrity and, whichever decision he makes, will be a decision which ought to be respected by the Australian community," he said.

Mr Heydon had been billed as a speaker on the invitation to the annual Sir Garfield Barwick address, which is named after the former High Court justice and Liberal MP.

Mr Heydon announced he had cancelled his appearance following Fairfax Media reports of his role in the Liberal Party fundraiser.

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