Role in coalition government with Labour could give party up to seven portfolios.
In four months, Green MPs could become government ministers for the first time in their party's 24-year history.
The final make-up of a Labour-Greens government would depend on several factors, in particular the role of NZ First in a possible coalition.
But if Greens are part of the government and portfolios are divided proportionally, they could expect to have up to seven ministers.
At their annual conference this weekend, MPs will discuss how ministerial roles could be allocated if they become part of a ruling coalition.
The Greens want significant portfolios in three areas - economic, social issues and environment.
Labour has ruled out giving Green co-leader Russel Norman the finance portfolio. He is expected to fight for the economic development role.
But he might not be trusted to manage a portfolio which includes oil exploration and mining. Instead, it could be split between two people, and Dr Norman put in charge of green investment or green innovation.
The Greens have unveiled a proposal for a $120 million Green Investment Bank, for which Dr Norman could be made responsible.
Co-leader Metiria Turei would seek a prominent social issues portfolio. It is understood that she has her heart set on being minister of education.
Labour is unlikely to give up major ministries such as social development or education, so she could instead get an associate role such as early childhood education.
Another possible position for her is minister for children - a new portfolio both parties want to set up.
Fourth-ranked MP Eugenie Sage could be a contender for the environment role, but is more likely to get conservation, local government, or Christchurch earthquake recovery.
It is almost certain that third-ranked MP Kevin Hague would get a significant portfolio.
The former West Coast District Health Board chief is highly regarded in Parliament, and is the Green MP Labour is happiest to work with.
He could be given the health portfolio, but would be more likely to be made the ACC minister.
Another contender for a place in Cabinet is Gareth Hughes. He's only 32 but has performed well as an MP.
Other MPs within reach of a ministerial portfolio are Catherine Delahunty (ranked sixth) and Kennedy Graham (seventh).