The PA news agency understands a meeting of the Scottish Cabinet approved the powersharing deal on Friday morning, but no details of the contents of the agreement have been made public.
The two parties have been locked in negotiations since May, after the SNP fell one seat short of an overall majority at the Holyrood election, and a deal could see the Greens in national government for the first time in the UK.
While both parties have said there will not be a formal coalition between the two, an agreement would see them work together on key issues, and could even see some Green MSPs appointed as ministers in Nicola Sturgeon’s Government.
On Sunday, Scottish Greens co-leader, Patrick Harvie, said the two parties had been “trying to finish off those last bits of discussion”.
Asked about the widely mooted co-operation deal, Mr Harvie resisted going into any details but told the BBC: “Everybody is very keen to know the outcome, I don’t think you have very long to wait.
“If we do agree something with the SNP it won’t be put into practice until our party members have had a vote … we’re trying to finish off those last bits of discussion.
“I hope very soon we’ll be able to publish something.”
A “New Zealand-style” co-operation deal has been discussed by Scottish civil servants.
The message, sent to members of the Scottish Greens earlier this month, said a New Zealand model, which has seen Green Party MPs in that country take on ministerial portfolios while not being in an official coalition, is being considered by civil servants and Government lawyers.
Scottish Tory net-zero spokesman, Liam Kerr, said the Green manifesto from May’s election was a “doctrine to start a war on working Scotland”, after it proposed a move away from North Sea oil and gas, and the end of new road-building projects.
Scottish Labour leader, Anas Sarwar, has challenged the Greens to stand against further cuts to council budgets.
He said: “If the Greens are to be anything more than simply the SNP’s lackeys, they need to rediscover their principles and fight for a greener Scotland rather than roll over to the SNP every time the going gets tough.”
A spokesman for the Scottish Greens said: “It’s no surprise that parties only interested in scoring political points would be alarmed about any suggestion of co-operation in the interests of people and planet.
“People vote Green to get results, and over the last five years the Scottish Greens have achieved more from our manifesto than Labour and the Tories combined. We will continue to do that, whatever happens.”
A spokesman for the First Minister said: “Following the SNP’s record landslide election win in May, the First Minister extended an open invitation to all parties to discuss areas where they thought they could work closely with the SNP in Government for the common good – in the face of the extraordinary challenges facing us such as the climate emergency and recovering from the pandemic.
“The fact that Labour and the Tories chose not to pursue that offer says far more about them than anyone else.”