Justice Minister Judith Collins is seeking advice on whether to hold an independent inquiry into the Teina Pora case.
Pora was convicted in 1994 of the rape and murder of Susan Burdett in her home. He was convicted again in a retrial in 2000; however new expert evidence suggests he may have been convicted on a false confession.
An increasing number of experts and some former senior police believe he is innocent.
A spokeswoman for Ms Collins said the justice minister had previously refused to comment on the case because it was potentially subject to judicial proceedings as Pora's lawyer, Jonathan Krebs, was considering seeking leave to appeal the case to the Privy Council.
However, Ms Collins said she was now seeking advice from officials after hearing Mr Krebs would prefer an inquiry be held before taking it to that point.