The difficulty for the Government is the part of the law it wants to change is a reserved provision, meaning it requires a 75 per cent majority in Parliament to change.
Section 35 of the Electoral Act discusses electoral boundaries and how they are set. It closely links sections on the Māori Electoral Option. As that section is reserved, it would require 75 per cent of MPs to agree on changes, rather than just a bare majority.
That means Labour and National would both need to agree to the change or repeal the provision. If successful, the change would be a win for Green Party Justice spokeswoman Golriz Ghahraman who is currently trying to change the law through a Members' Bill.
Faafoi announced the Government would review this part of New Zealand's electoral laws last year, with a view to having it finished before the election.
On Wednesday, Faafoi said the Government had consulted with other parties, and received their feedback.
"We've heard back we've tried to deal with some of their concerns, but we'll have more to say on that soon," he said.
National's Justice spokesman Paul Goldsmith said his party would not be backing the change as it currently stood, saying he had concerns people could switch between rolls before elections, influencing the outcomes in marginal seats.
"The proposal is to have an exclusion around a byelection so people can't change between rolls during a byelection. We agree with that but we think the logic applies equally to general elections, because there is frankly the risk that people could switch between rolls in marginal seats during a general election campaign," he said.
"We're open to greater flexibility in the system, but we think that needs to be an exclusion around three or four months around a general election," he said.
Goldsmith said he had suggested a change to the Minister to change the legislation along these lines, meaning people could not switch rolls close to a general election.
He said National had not had a reply on whether the Government would adopt the suggested change, although Faafoi told media he had tried to "deal with" concerns raised by other parties.
Ghahraman has been pushing for this change as part of a range of reforms to electoral laws included in her electoral law reform Members' Bill, which was recently drawn.
She called on National to back the changes.
"Electoral reform should not come down to party politics. We would call on every party to make their positions according to the recommendations of experts.
"This is one of the changes - the Māori electoral change option issue has come up again and again as something that needs to be reformed," she said.
Her bill will also take a look at the reserved provisions of the Electoral Act. Ghahraman said the present episode shows the reserved provisions making it difficult for a Government to expand access to voting, something the law should encourage.
"[The issue] is an interesting one to highlight that our entrenchment laws are ad hoc. The term five years seems to be completely random," she said.
Act leader David Seymour said he had received the draft bill from Faafoi.
"We will consider it in Caucus before offering our feedback," Seymour said.
"We're open to flexibility, but not at the expense of a free and democratic electoral system," he said.
Te Pāti Māori was approached for comment.