The deal would see the Greens move into government for the very first time anywhere in the UK, following several months of negotiations with Ms Sturgeon’s party.
Opposition parties challenged the Greens not to become “the SNP’s lackeys” ahead of an expected co-operation agreement between the two parties.
Scottish Labour leader Anas Sarwar said: “If the Greens are to be anything more than simply the SNP’s lackeys, they need to re-discover their principles and fight for a greener Scotland rather than roll over to the SNP every time the going gets tough.”
Mr Sarwar added: “The grim reality is that this coalition isn’t a surprise, it is just formalising what we’ve seen for years – Nicola Sturgeon and the SNP hammering our public services with cuts, and the Greens nodding along.”
Ms Sturgeon told the Scottish parliament in May that talks would begin on a co-operation agreement between the two parties after her party fell one seat short of a majority in Holyrood.
With the Greens winning a record eight seats at the May election, the deal is expected to formalise a majority in favour of independence, as well as allowing the two parties work together on specific policies.
The talks appeared to be winding down on Thursday evening. An email sent to the Scottish Greens’ members said the wording of the deal would be provided to them by August 20.
The email sent to Green members said the final agreement was being mulled by civil servants and lawyers because a “New Zealand-style” deal – which would see a Green MSP as a minister in government – has never been in place before in Scotland.
Last week Ms Sturgeon called on Boris Johnson to “reassess” plans for the new Cambo oil field near Shetland following an outcry by climate campaigners.
The SNP leader said the UK government should reconsider drilling licenses for the waters around Shetland where no development had yet taken place.
Ahead of the co-operation agreement, the Scottish Tories also issued a warning to the SNP government. Tory net zero spokesman Liam Kerr said the recent Green manifesto was a “doctrine to start a war on working Scotland” after it proposed a move away from North Sea oil and gas.
Greens have insisted their proposals to end extraction and exploration in the North Sea would be part of a “just transition” and would include retraining for the workforce in the north east.
“Patrick Harvie will push for the end of the oil and gas industry at the first chance he gets, abandoning the 100,000 jobs which depend on it,” said Mr Kerr.
He added: “This deal is just another way for the SNP to push for another divisive referendum. The Scottish Conservatives will stand up for workers and families against this nationalist coalition of chaos.”