The 46-year-old stood down moments after handing down the NT budget on Tuesday, saying his head and heart were no longer in the job.
His loyal deputy and acting chief minister Nicole Manison declared the Territory Labor caucus would announce a new leader on Friday.
But it may not be that simple.
If two or more Labor parliamentary members nominate to contest the leadership and that person has 20 per cent or more support from the caucus, the ballot must be broadened to include rank and file members.
That would likely take weeks, potentially leaving the NT with an acting chief minister until well after the federal election.
None of the 14 caucus members have publicly nominated for the top job but three possible contenders have emerged: police minister and right faction member Ms Manison, as well as Health Minister Natasha Fyles and backbencher Joel Bowden - who are both from the left.
A former union boss and AFL player, 43-year-old Mr Bowden is unlikely to receive caucus support given his lack of parliamentary experience.
The contest is more likely to be between Ms Manison and Ms Fyles, both 43.
The left and right factions each have six members with Attorney-General Selena Uibo and recently elected Dheran Young unaligned.
Renewables and Energy Minister Eva Lawler was tight-lipped about leadership race when she fronted the media on Thursday.
"There is considerable depth in the Labor team. The leadership will be decided on Friday," she said.
"I'm not betting on anyone (but) I think everyone understands I'm on the right in Labor and I'll be working to support whoever goes forward on the right."
Asked about Mr Bowden's aspirations given he has not held a ministry, Ms Lawler said it was a vital for chief ministers to have such experience.
"Being chief minister is hard work, let alone with the overlay of COVID, which makes the job even more complex," she said.
Political economist Rolf Gerritsen believes the factions will do a deal before Friday's vote.
"The votes are about even in caucus. They will agree that Manison remains chief minister, which makes the deputy position vacant and they will appoint someone from the left," he told AAP.
"My guess is Bowden or Fyles will be deputy."
Federal opposition defence spokesman Brendan O'Connor refused to be drawn into the faction stoush, saying it was up to the local government members to decide who should be the next chief minister.
"They're the people who understand the government here. They 're ones intimately aware of their colleagues' capacity and it's entirely up to them who they choose," he said while campaigning in Darwin.
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