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.