Speaking to BBC Radio’s Good Morning Scotland programme, Ms Slater suggested that a formal deal with the SNP could be in place after the Summer recess.
She told interviewers that her party and the SNP shared several “common goals”, including on policy areas including housing, renewable energy investment, job creation and recovery from the Covid-19 pandemic.
Her latest comments come after she said the SNP and Greens were “worlds apart” on climate change policy last month.
With just a fortnight to go before voters headed to the polls, Ms Slater told The i that “just about the only policy we have in common is independence”.
But on Thursday morning, she hinted that the Scottish Greens were interested by the situation in New Zealand, where Green MPs hold ministerial positions, but are not formal members of Jacinda Ardern’s Labour cabinet.
“So they have a cooperation agreement that means that those Green ministers take responsibility for certain very specific areas,” Ms Slater said, “that works very well in New Zealand.”
The 46-year-old warned it was still “very early days” in the talks, adding that any changes to the make-up of the Scottish Government - or Ms Sturgeon’s cabinet - would likely only take effect in the Autumn.
What will the Scottish Greens gain?
The SNP and the Scottish Greens are seeking a Cooperation Agreement - an arrangement somewhere between a basic confidence and supply deal, like that formed by Theresa May’s Conservatives and the DUP in 2017, and traditional coalition.
Ms Slater said her party hoped to create a “different kind of working environment in the Scottish Parliament” and to get key Green priorities onto the Scottish Government’s agenda.
She hinted that cooperation with the SNP was likely to come at the price of Green involvement in managing Scotland’s economic recovery from coronavirus, as well as control over management of the climate crisis.
“It's very exciting that we do have a new kind of politics on the table - a politics of cooperation, and consensus building, and finding common ground,” she added.
Covid breach after Bute House talks
Ms Slater also confirmed rumours that she and her co-leader, Patrick Harvie - along with senior Green MSP Ross Greer and another man - had just left talks at Bute House when they breached coronavirus rules at a bar in George Street, Edinburgh on Tuesday.
Current restrictions in Level Two areas, like the Capital, mean only three households are allowed to be together in an indoor hospitality setting.
And while MSPs are able to travel for work, rules make clear it should not be conducted in a hospitality premises.
“That was that was a mistake, we're absolutely kicking ourselves about that and I'm really sorry that happened,” Ms Slater said.
The group of four had “been together all day” in a series of meetings with Scottish Government officials at the First Minister’s official residence, when they made the “split-second decision” at 5pm to sit inside the bar, rather than outside.
“It was definitely a mistake. You're right to call me out on it.
“I unreservedly apologise for making that mistake - we're absolutely kicking ourselves about it.”