Teina Pora's legal team say he will not be pushed into accepting the Government's compensation offer immediately.
Mr Pora was awarded $2.5 million compensation and received an apology this week for being wrongfully convicted of rape and murder after being imprisoned for 21 years.
The offer did not include an inflation component, despite a recommendation to do so from retired High Court judge, Rodney Hansen, QC, who made the decision on compensation.
Mr Pora's team say they are now considering challenging the inflation decision.
However, Mr Pora's team say their client has been asked to immediately accept or decline the offer made, meaning that if he wishes to challenge even a small part of the offer he has to first decline in full - at least in the meantime.
"We think that is unfair," a statement said. "Mr Pora is under immense pressure of finances and emotion ... the decision whether to challenge this aspect is complex and will take time to reach."
The team have written to Justice Minister Amy Adams to invite her to moderate the Deed of Release to allow Mr Pora to receive the sum currently offered but also allowing him the opportunity to challenge part around inflation.
"This appears to us to be an eminently fair approach. It allows Mr Pora the ability to consider his position in an unpressured way, while allowing the Government the comfort of knowing that any Court challenge would be limited to a discrete issue," the statement said.
"It also takes into account the enormous power imbalance at play between Mr Pora on the one hand and the Government on the other."
The team said Mr Pora had been humbled by the outpouring of support for him, and the sense the Government should have adjusted his payout for inflation.
Justice Minister Amy Adams said she received Jonathan Krebs' letter at 3.30pm today.
"Mr Pora's legal team have requested an amendment to the standard process which is that a Deed of Release to the applicant's claims against the Crown is signed and then the payment made. I'm more than happy to consider their request and have asked for advice on the matter.
"It is important to note that the compensation offer is not in any way time bound."
The Justice Minister was pressed by Labour's justice spokeswoman Jacinda Ardern as to why an inflation adjustment was not approved during a select committee hearing at Parliament today.
Ms Adams said the inflation adjustment amount could vary considerably, depending on what calculation method was used.
"I have received some rough calculations ... you can cut it any number of ways. It could be anything from ... $50,000 to $400,000, to $700,000 if it was inflation adjusted."
Ms Adams said the guidelines, introduced by Labour, did not provide for inflation adjusting.
"We had to be mindful of the eight other people who have been compensated under those guidelines who haven't had inflation adjusting."
Other components of the compensation offer were made in real dollar terms, Ms Adams said, but Cabinet was comfortable with the $100,000 per year figure.
"The $100,000 actually sits very well in terms of international measures for the amounts of compensation.
In the UK, if you have had more than 10 years in prison, your total compensation is capped at one million pounds, if you are in the US the annual rate is somewhere between $18,000 and $100,000, across different states."