The Greens usually go third in the weekly questions’ session, with co-leaders Patrick Harvie and Lorna Slater taking turns to question Nicola Sturgeon.
But the Scottish Tory chief whip, Stephen Kerr, has written to Presiding Officer Alison Johnstone – who was elected as a Green MSP in May’s election – to urge her to remove the question.
The two parties will announce a co-operation agreement on Friday after months of negotiations, and Green MSPs could be given ministerial office as a result.
Mr Kerr claims, if the two parties form an alliance, leaders will give the First Minister an easy ride.
“It would make a mockery of the Scottish Parliament if members of the Government were allowed to tee up Nicola Sturgeon with waste-of-time queries to help her run the clock out at First Minister’s Questions,” he said.
“Proper opposition scrutiny of the SNP-Green Government is essential.
“How will softball questions from Patrick Harvie, drafted in Nicola Sturgeon’s handwriting, hold the government to account?”
He added: “The Greens can’t have their cake and eat it. Now that they’re officially forming a nationalist coalition of chaos, they can no longer even pretend to be an opposition party. That would undermine Scottish democracy.
“We have formally started proceedings with the Scottish Parliament and Presiding Officer to remove the Greens from their position at FMQs, in line with the precedent set by the Labour-Lib Dem government.”
Both sides have said any agreement will not be a formal coalition – as was the case between Labour and the Lib Dems in the first two terms of the Scottish Parliament.
If the Presiding Officer did strip the Greens of their slot at FMQs, then only the leaders of Labour and the Tories would be able to scrutinise Ms Sturgeon.
Mr Kerr has also pushed for the party to be stripped of the ability to call opposition debates and for Green spokespeople to lose the ability to question ministers following government statements.
Opposition parties have attacked the Greens and the SNP for the deal, with Tory net-zero spokesman Liam Kerr saying the Greens’ manifesto is 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.
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,” Mr Kerr said.
“They have no interest in energy transition. They want an unfair conclusion of our North Sea sector which is developing the very means to hit net zero.”
Labour leader Anas Sarwar has challenged the Greens to stand against further cuts to council budgets.
“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,” he said.