The Greens, who often hold the deciding vote in Holyrood, have released a statement saying they will back the vote should the legal advice in relation to Alex Salmond’s judicial review be kept from the harassment complaints committee.
The decision comes as the committee is set to issue its third section 24 notice to Mr Salmond’s solicitors Levy and McRae on Tuesday.
The former first minister had suggested to the committee during his evidence session on Friday they could issue the notice to compel his solicitors to hand over the evidence they hold in relation to the judicial review and the allegations of conspiracy against him.
It comes after the Scottish Conservatives lodged a motion of no confidence in Mr Swinney on Monday after the Scottish Government missed a deadline to publish the advice.
The Salmond inquiry has repeatedly asked the Scottish Government for sight of the legal advice and the SNP lost two votes calling for it to be released in unprecedented defeats in Holyrood last year.
Despite Scottish Conservatives hoping for the vote in Mr Swinney to take place on Tuesday, it is understood it is most likely to happen on Thursday after the First Minister attends the Salmond inquiry on Wednesday.
The motion is now backed by all opposition parties, with the publication of the legal advice now the only way out of a highly damaging defeat for the Scottish Government.
If it is lost, it is a convention for ministers subject of the motion to step down from their posts.
In a statement, Scottish Green MSPs said: “The Scottish Greens have previously voted to ensure that the Government's legal advice is made available to the committee inquiry, and this remains our position.
“The Committee on the Scottish Government Handling of Harassment Complaints has made it clear that it needs access to the Scottish Government’s legal advice on its investigation into Alex Salmond to fulfil their remit, and Parliament has repeatedly backed the committee.
“The Scottish Government now has just days left to agree the terms of the committee's access to the information requested. Reaching an agreement on this which is acceptable to the committee is clearly the only way to avoid a vote of no confidence.
“The Conservatives have been shameless opportunists throughout this process, but the Scottish Greens will always defend the integrity of the Scottish Parliament and its ability to hold Government accountable.
"This inquiry should be focused on identifying what went wrong with the investigation into sexual harassment, and on the interests of the women who were failed by the process and others who will need to have confidence in the complaints process in future.”
The committee is examining the botched handling of harassment complaints against Mr Salmond by the Scottish Government, which led to a £500,000 legal bill after the Government conceded a judicial review challenge on grounds the process was “tainted by apparent bias”.
Mr Salmond was also acquitted of sexual offence charges in a trial last year.