Justice Minister Judith Collins says it would be easier for Teina Pora to get his conviction overturned by the Privy Council than by royal pardon.
Teina Pora was convicted in 1994 of the rape and murder of Auckland woman Susan Burdett, crimes he says he did not commit.
The Police Association wants the case reviewed citing concern among senior detectives about the conviction.
Ms Collins says it would be better for Pora to pursue the Privy Council option first, because it would be easier to get his conviction overturned by a court.
"Rather than a not guilty decision which a court can give, a pardon is essentially saying that there is a higher standard and Mr Pora would have to show that he was likely to be innocent. So that's why I suggest he goes down the Privy Council route first."
Earlier, Ms Collins said it would be constitutionally unsound for the Government to issue a pardon to Teina Pora while he is waiting to have his case heard by the Privy Council.
She said if the appeal did not go ahead, Pora could then apply for a pardon.
Pora's lawyer Jonathan Krebs says an application for leave to appeal will be filed in the next couple of days. He says if that is granted, he would expect the case to go before the Privy Council late this year or early next year.