Community Services Minister Joy Burch or Education Minister Chris Bourke face at least temporary relegation to the Assembly backbenches to make room in cabinet for Greens MLA Shane Rattenbury.
Chief Minister Katy Gallagher plans to expand the ACT executive from five to six ministers, but such a move would require the passage of a law through the Assembly.
Ms Gallagher said this meant the new government would need to start with five ministers.
The Chief Minister and her deputy Andrew Barr will take up two of the Labor ministerial positions and the third is expected to go to veteran MLA and minister Simon Corbell.
The eight-member Labor caucus will have to decide whether the final spot goes to Ms Burch or Dr Bourke.
Ms Gallagher said the growth in the ACT's population had increased the government's workload.
''I think we've got to the point where if people want good government and they want government to be able to respond all the time, then six ministers is a necessity,'' she said.
''It's not like I'm afraid of hard work - I'm happy to work very hard - but it comes to how much time physically and intellectually you can put into a portfolio.''
Opposition Leader Zed Seselja said he did not object in principle to the expansion of cabinet but wondered why Labor had not moved to do this earlier. ''They could have done this at any time but they've never taken it forward. I suspect it's been more about their concerns, could they fill six ministries,'' he said.
Under Labor's power-sharing agreement with the Greens further reform of the territory's political system will also be considered, with an expert committee to look at options for expanding the size of the Assembly.
Mr Rattenbury said on Sunday he was looking forward to being the first Greens member of an ACT cabinet.
''Obviously having a Green sitting inside a Labor cabinet has its challenges but I think the will is there to make it be successful,'' he said.
Mr Rattenbury believed he would be able to work constructively with his Labor colleagues, even if he sometimes spoke out publicly against government policies.
''I think there's room to have a different view without necessarily disrupting the flow of an agreement,'' he said.
During the previous Assembly the Greens were sometimes upset when ministers introduced policies without acknowledging they were contained in the Labor-Greens agreement.
Under the new agreement, ministers will have to acknowledge the fact that they are implementing Greens policies.
The government has also agreed not to make ''disproportionate'' budget cuts to portfolios to which Mr Rattenbury is appointed.