ACT Greens leader Shane Rattenbury says the party should be entitled to three ministers in cabinet after winning six seats.
The party will not be gunning for the deputy chief minister role in negotiations with Labor, but Mr Rattenbury appears open to serving as attorney-general.
Chief Minister Andrew Barr last week indicated he would be willing to appoint up to two Greens ministers.
Labor and the Greens are nutting out the details of a parliamentary agreement to form government, but Mr Rattenbury says he won't be using "megaphone diplomacy" to negotiate.
The negotiations will determine what role the Greens will play in cabinet and which election commitments will be part of the government's agenda.
"I think it's useful we go into today's discussions with open minds," Mr Rattenbury said.
Chief Minister Andrew Barr has previously said Mr Rattenbury would be considered for attorney-general after Gordon Ramsay lost his seat in Ginninderra.
Mr Rattenbury indicated he would be open to taking on the role.
"There are a number of areas we are particularly keen to work on, and certainly justice policy has been a key issue we talked about in the election campaign," he said.
"Whether it's as attorney-general or a different role, that will be part of the conversation."
Mr Rattenbury wouldn't reveal which ministries the party would be keen to take on.
But he has previously said it would want to have a say in the areas of climate change, environment, planning and housing.
"That's an area for discussion; we don't particularly want to signal via megaphone diplomacy how we want to go about these discussions this afternoon," Mr Rattenbury said.
"We'll sit down, there are a number of areas we are interested in, I think it's kind of obvious through the issues we've talked about through the course of the election campaign.
"But there's a lot of back and forth to be had."
Mr Rattenbury said the party would be gunning for three ministers in the new government.
"With six out of 16 positions in the two governing parties it is three-eighths of the government, and I think it would be reasonable for the Greens to get three ministries in that context," he said.
Despite Mr Rattenbury's name being floated for deputy chief minister, he said it wasn't a priority for the Greens.
"We're not really here for titles, we're here to get the job done," he said.
"We're more interested in the issues than the job titles that are being talked about by others.
"It's not an ask we've made."