The Green Party will decide soon whether to wait until July to appoint a new female co-leader or to start the process earlier - and there could be four contenders for the job.
The party has been lead by James Shaw alone since former co-leader Metiria Turei resigned over the fallout of her admission to historic welfare fraud in the lead up to the election.
The party's executive will meet on Tuesday night to decide whether to wait until the party's Annual General Meeting, likely in July, or hold a Special General Meeting or postal ballot to elect a new co-leader earlier.
Those considered likely to contest it include Julie Ann Genter, Marama Davidson, and possibly Eugenie Sage and Jan Logie. Of those, only Genter and Sage are ministers.
The Green Party members elect the co-leaders and may not consider a ministerial role a major factor - Russel Norman was not in Parliament at all when he was elected over sitting MPs Nandor Tanczos and David Clendon.
However, it would be unusual for a co-leader not to be a minister when other MPs were.
Davidson said she had no view on whether the party should wait until the AGM or go earlier.
"I am strongly considering putting my hat into the ring. That's definitely me not ruling it out."
Genter said she was yet to make a decision. "I think when we have some idea about the dates and have a conversation internally I would have a better idea."
Eugenie Sage - who was part of the Greens' team during government negotiations with Labour - said she too had not made any decision. "I'm still getting my feet under the table as a minister."
Logie did not respond to requests for comment.
Green Party co-convenor John Ranta said the leadership was usually voted on at the party's Annual General Meeting after a campaign period for the contenders. It was possible the election could be done earlier by a Special General Meeting or even postal ballot.
The AGM would not take place until July - which would mean an 11 month gap in the role.
"So that will be one of the factors people are thinking about.
But we've got a number of MPs who are now filling ministerial roles and it's a whole new world for us in a lot of ways, being in Government.
It's a long time to go without a co-leader but at the same time we don't want to rush a decision especially when we've got a lot of other things going on. There are good reasons on both sides."
There was speculation the Greens could seek to stand only one contender to prevent the need for a vote, but that would invite a backlash from the members.
Co-leader James Shaw said while he did not know who might contest it, there had been no discussions about trying to arrange for only one person to put their name up.
Previous leadership contests were also a good chance for party members to get involved in the party. That could be important with the Green Party's vote so low after the 2017 election.
Ranta said the party's rules did not provide for an interim co-leader to be appointed - such as by the executive or caucus - and he was reluctant to do so.
"Theoretically it might be possible for the party executive to determine to do something like that but it would be extraordinarily risky, I would say, from an internal point of view to appear to undermine the internal democracy of the party, especially around such an important position."
The Green Party's leadership campaigns can be time consuming - in the past contenders had to travel around the country for up to two months before the vote to speak to meetings of Green Party members.