"That indicates that we're making good progress," she said.
Today was the third time the Greens leadership and senior party officials have met with the Labour camp.
A spokesman for Prime Minister Jacinda Ardern said the conversations continued to progress well and were still scheduled to wrap up by Friday.
Labour won an outright majority in the election, securing 64 out of 120 seats.
That number could go even higher once the special votes are counted.
Despite this seeming lack of leverage for the Greens, Shaw told media that his party was "hoping to be able to form a Government".
This could, however, mean a number of things. For example, the Greens could help form the Government by providing confidence and supply like they did last term.
It could also mean they are given a number of undersecretary positions or it could mean some Green MPs are put into Cabinet and the two parties form a coalition.
The latter is, however, the most unlikely option as Ardern has previously iterated it is the Labour Party that has a mandate to govern.
Shaw would not comment on speculation that he has been offered the Climate Change portfolio – a portfolio he held in the last Government.
The talks will continue for another two days before the Greens leadership takes an offer back to a committee of its members to vote on.
Shaw said he and Davidson would only be putting up an agreement to members that they think is worth putting up.
Davidson said the talks today were about narrowing things down and getting to the "final point".
Shaw said: "We are in the concluding stages – we are now narrowing things down, rather than broadening things out."
