The unprecedented move, as first reported by the Sunday Times, follows the Scottish Government’s refusal to publish the legal advice given by James Wolffe on the judicial review into the investigation of complaints against former first minister Alex Salmond.
A no-confidence vote against deputy first minister John Swinney is also reportedly being considered, in an attempt to force the government to comply with a parliamentary motion telling it to publish the advice.
Scottish Conservative spokesman Murdo Fraser MSP claimed the situation had “become an absolute farce”.
He said: “The committee and the Parliament should explore every option to force the government to release the legal advice that resulted in the loss of £500,000 of taxpayers' money.
"Whoever is blocking the release of this advice – whether it’s the First Minister or the Lord Advocate – should explain to the public why they think these documents should remain secret and the government should go without scrutiny.
"This committee was set up in January 2019 and has been calling for evidence repeatedly throughout the course of the last nine months.”
Scottish Labour's deputy leader Jackie Baillie said: "It is becoming apparent that there may be competing interests in the government unable to decide between themselves whether to publish this material or not."
The botched handling of the complaints made by female civil servants against Mr Salmond led to taxpayers being forced to pay the former first minister £500,000 in legal expenses.
Despite this, ministers continue to insist they should not have to release private advice from lawyers regardless of Holyrood passing a motion urging them to do so.
A Scottish Government spokesperson said: “The Deputy First Minister has clearly set out in his letter to the committee the detailed consideration that the government is giving to this issue and also the extensive steps that are being taken to secure the release of further documentation.”
MSPs on the inquiry could now face a lengthy wait to get access to legal advice at the heart of the probe – even if the Scottish Government makes it public.
Mr Salmond was cleared of a string of sexual assault charges at the High Court in March.
This came after he won a judicial review against the Scottish Government over its handling of internal complaints made against him by two civil servants.
The Scottish Government last week lost a vote at Holyrood, which called on it to publish the legal advice it received relating to a judicial review brought by the former first minister over its handling of that internal probe.
It comes as ministers were claimed to be taking expensive legal action to prevent the disclosure of just one paragraph of First Minister Nicola Sturgeon's communications with a senior civil servant over complaints against her predecessor.
Discussing a zero tolerance approach to sexual harassment, the Scottish Government has decided to take the case to the Court of Session while choosing not to disclose a few lines in a letter sent to Permanent Secretary Leslie Evans.