A legal expert says unions have a chance of appealing over Dyson Heydon's decision not to stand down from the royal commission.
The ACTU and other unions are weighing up the prospects of a court challenge to Mr Heydon's rejection of their application for him to step down over perceived bias.
Unions claim Mr Heydon's acceptance of an invitation to speak at a Liberal Party function, from which he withdrew last month, gave a perception of political bias.
Adelaide University law lecturer Dr Anna Olijnyk said Mr Heydon's ruling was sound, but there was a chance unions could win an appeal to the Federal Court.
"There are clear cases of bias sometimes. There are clear cases where there's no argument for bias. This one is right in the middle I think," Dr Olijnyk told ABC radio.
"So they've got a chance."
Labor will also seek Senate support next week for a motion to petition Governor-General Sir Peter Cosgrove to withdraw Mr Heydon's commission.
Workplace Minister Eric Abetz says such a motion was a stunt and would have no legal consequence.
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