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The process surrounding the application was discussed by the Cabinet when Justice Minister Judith Collins updated her colleagues.
This follows her rejection in December last year of the review by Ian Binnie, a former judge of the Canadian Supreme Court.
Ms Collins said he had delivered a report with serious errors about the New Zealand law of evidence and she could not make a recommendation to the Cabinet based on it.
Mr Binnie found that on the balance of probabilities Mr Bain was innocent of murdering his parents, two sisters and brother in Dunedin in 1994 and had been wrongfully imprisoned for 13 years.
Former New Zealand High Court judge Robert Fisher peer reviewed Mr Binnie's report for Ms Collins and she did not rule him out as a person who might conduct a further report.
Mr Key said Ms Collins would return to the Cabinet with other options that included asking Dr Fisher or someone else to do more work.
Asked if there would be a second report, he said "most probably".
Mr Key said that while the cost of the process was important, it was necessary to reach a robust conclusion by which New Zealanders could understand why any decision had been reached.
Mr Bain's longtime supporter Joe Karam said last night that Mr Binnie's report "should be honoured".