At least 104 delegates – some 75 per cent of those meeting – need to agree to the deal for the party as a whole to adopt it.
Speaking to media after another round of negotiations with Labour's team this afternoon, co-leader Marama Davidson said the talks were going well.
"We will look to have an announcement on Sunday."
This means the formal negotiations with Labour will have concluded in less than a week.
In the last election, the Greens announced that its members had backed the Supply and Confidence deal with Labour just hours after NZ First leader Winston Peters chose the Government.
Shaw said today that the Greens had actually concluded negotiations with Labour a week prior – "but we were waiting for Winston".
According to the Greens' constitution, at least 75 per cent of delegates need to agree to the deal offered by Labour for it to be accepted by the party as a whole.
If they don't accept it, the Greens will go into opposition.
It's likely the call to the delegates will be held on Saturday – given talks with Labour finish on Friday and the announcement is expected on Sunday.
Davidson said it was hard to say how long it would take their members to agree to, or vote against, a deal.
"We allow for the delegates to have a good look at what's before them – it's a big decision."
Throughout the negotiations, Shaw and Davidson – along with chief of staff Tory Whanau and co-convenor Wiremu Winitana – have in contact with a group of senior party members to discuss the negotiations.
That group consists of former and current MPs, such as Eugenie Sage, Elizabeth Kerekere, Julie Anne Genter and Mojo Mathers, as well as leaders from the party.
According to Shaw, that group is a "sounding board".
The negotiating team asks the group if they missed anything, what else needs to be explored and "how do you think this will go down with the members".