Justice Minister Andrew Little wants eligible voters to be able to register to vote on election day by the time the country goes back to the polls in 2020.
Mr Little says he's worried a select committee inquiry into the 2017 election could go on too long to make the change by 2020 and if that looks to be the case he'll seek Cabinet support to speed it up.
Currently eligible voters have to enrol by the Friday night before the election.
Both the Labour Party president Nigel Haworth and the Electoral Commission chief electoral officer Alicia Wright told MPs on the justice select committee they'd like the change by 2023.
Mr Little is keen to go one better.
"The Electoral Commission has commented on it in their review of the 2017 election, they have said that this will be a helpful thing to do. So on the basis of that let's see if we can get it done in time for 2020,'' Mr Little said.
He's instructed his officials to look into the changes with a "view to that law change being made in time for 2020''.