The ACT Greens emerged as 'kingmakers' at the last territory election and expect to continue that role after this weekend's polls.
The party rose as a major political force four years ago, winning four seats in the 17-member parliament before supporting the seven-seat Labor side to government.
A Canberra Times-Patterson poll published on Thursday shows they're likely to retain their seats when the votes are counted after Saturday's election.
If so, the Greens will again be in position to govern alongside Labor or the Liberals victors.
Chief Minister Katy Gallagher's Labor government has come under fire from the Liberal opposition for being 'in coalition' with the Greens.
But Ms Gallagher says there have been 'plenty of votes' in the legislative assembly over the last term when the two parties disagreed.
'But when it comes down to the day-to-day delivery, I think people will recognise that there's been a co-operative relationship there,' she told AAP in an interview.
'They expect us as elected representatives to work with whoever gets elected.'
Liberal leader Zed Seselja says territorians are disappointed with the Greens.
'There are people who voted Green for the first time last election and who say, I haven't really got much out of it',' he said.
Mr Seselja ruled out offering the Greens a ministry - unlike in 2008 when he put up both the deputy chief ministership and another ministry as incentives for their support.
While he didn't go so far as to say he wouldn't negotiate, Mr Seselja isn't certain the Greens would be onboard anyway.
'I suspect they wouldn't negotiate with us,' he said.
Greens leader Meredith Hunter has told both sides her party is ready to negotiate, whatever the outcome.
'Our door is open to both parties,' she said.
'From our point of view, we are waiting for that poll result. We'll see how those numbers fall.'
Ms Hunter says the Greens don't see a cabinet position as an end in itself.
'Policy and getting outcomes on the ground are the most important things for us,' Ms Hunter said.
'That would be the start of any negotiations.'
The first ACT Greens member of parliament was elected in 1995.