Federal Opposition Leader Bill Shorten concedes the Royal Commission into Trade Union Governance and Corruption could continue if a suitable replacement for Dyson Heydon is found.

The position puts him at odds with the union movement, which has called for commissioner Dyson Heydon to resign and the commission be scrapped.

The Australian Council of Trade Unions (ACTU) seized on details that the former High Court Justice had agreed to speak at a Liberal party fundraiser.

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It has argued the commission’s entire fact-finding process has been flawed, and should end with Justice Heydon’s resignation.

On Friday, the commissioner will rule on an application by the ACTU to have him disqualified from the position.

The commission says if Dyson Heydon does not deliver his judgment at the end of tomorrow’s proceedings, he will deliver his finding early next week – possibly on Tuesday.

In the event Commissioner Heydon does rule himself out, Mr Shorten said he would not block moves to appoint a replacement.

“The key issue here is the conduct of the captain’s pick, the royal commissioner,” he said.

“If they find another royal commissioner, so be it.”

The Opposition Leader remains concerned about the conduct of the commission, and that it is biased against the trade union movement.

“I’ve always said that I’d be willing to cooperate with this royal commission, but let’s call it as it is,” Mr Shorten said.

“The Labor movement has had grave concerns that Tony Abbott set up a political royal commission to spend millions and millions of taxpayer dollars … to engage in a political witch hunt.

“When it comes to this current crisis engulfing the royal commission, that is not a crisis of Labor’s making, it is a crisis of Mr Abbott and his captain’s pick.”

– ABC