Federal Labor will press ahead with a Senate motion calling on the governor-general to dismiss royal commissioner Dyson Heydon amid new claims a prominent trade union witness was briefed by inquiry lawyers.

Kathy Jackson, long hailed as a whistleblower from the Health Services Union, was provided in advance with details of what she would be asked at the commission into trade union corruption, The Australian reported on Tuesday.

The Senate is expected to consider a Labor motion later on Tuesday that asks Governor-General Peter Cosgrove to revoke Mr Heydon’s commission on the grounds he has failed to uphold standards of impartiality.

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Senior Labor frontbencher Stephen Conroy said the report proved there was a “clear case of bias”.

“Any fair-minded senator would have to say that Heydon should go, that (counsel-assisting) Stoljar should go, that the staff should go,” he told reporters in Canberra.

He called on the crossbench to examine the file note of July 25, 2014 between the commission’s legal team and Ms Jackson.

The commission was “fatally compromised” by the document.

Opposition workplace relations spokesman Brendan O’Connor said the “damning revelations” clearly showed the commission was tainted and biased.

“Kathy Jackson has been coached to give testimony … and indeed been treated with kid gloves,” he told reporters in Canberra, saying that contrasted with the treatment meted out to other witnesses.

“This is a biased commission, one that’s being used for improper purposes.”

Employment Minister Eric Abetz labelled the motion “disgraceful” and urged Labor to drop it.

Senator Abetz said he did not know where the report about Ms Jackson came from, noting she had complained about being ambushed by the commission.