Ms Coatsworth said contestants would also be subject to a code of conduct to adhere to during the run-off.
David Cunliffe and Grant Robertson ate both expected to put their hands up for the job although both are yet to confirm that.
Andrew Little could also be a contender.
It will be the first leadership change under new rules which give the members and unions a vote.
Previously the leader was elected by the caucus.
The vote will be weighted so the caucus vote counts for 40 per cent, the members for 40 per cent and the unions 20 per cent.
Ms Coatsworth said it was a historic occasion for the party since major reforms last year.
"We expect the leader will have a strong mandate."
Ms Coatsworth said it was caucus' decision whether to put up only one candidate or more - but sent a clear warning that the members would not be happy if caucus did come to a deal which resulted in only one contestant.
That would deprive the members of a chance to vote. She said she would endorse the new leader if only one was put up, "but there is a widespread view among the membership that this is an important process, selecting the next Prime Minister."
She said they would welcome the opportunity to vote on it in a public process rather than have it decided "behind closed doors."
Ms Coatsworth would not give membership numbers, but said it would mean between 40,000 and 50,000 members of the five affiliated unions or the party would be able to vote.
The unions had agreed with the Council not to vote as a bloc.
Meanwhile, former Labour Party President Mike Williams has slated some of the blame for David Shearer's problems down to the party's ruling Council for failing to support him.
Mr Williams said on Radio New Zealand this morning that he did not believe the New Zealand Council had supported Mr Shearer.
"I don't think the party supported David Shearer and by that I mean the Council, as fulsomesly as they could."
He said Mr Shearer had probably believed the Council wasn't fully behind him. He said when he was Party President he had taken the view that he should throw his full support behind whichever leader caucus had chosen.
"I always took the view that, whatever the caucus dished up, I would defend the leader.
And I did that. There's a lesson out of this that the party's Council has to get really firmly behind whatever the process delivers and I don't think they were in that position before."
He said it had been easy for him because he had known Helen Clark - who led the party when Mr Williams was President - for 30 years.
The Party's Council had passed through major reforms to the way the party was run under Mr Shearer's watch, including the requirement for a leader to get the support of at least 60 per cent of caucus in a regular three-yearly confidence vote. That measure was seen by many as an attempt to undermine Mr Shearer.
The Council had also backed the controversial 'man ban' proposal to restrict some electorates to women-only candidates, and institute a quota of at least 50 per cent of women in caucus.
Mr Shearer had persuaded the Council to back down on that.
