Discussions are believed to have taken place within the Scottish Government on the merits of removing schools from local government control, The TESS understands.
Buffeted by political embarrassment over their failure to make headway with their flagship policy to reduce P1-3 class sizes to 18, ministers have been considering their options - direct rule being one of them.
Although this would fly in the face of the concordat partnership between local and central government, it is a reflection of the frustration felt, particularly by Education Secretary Fiona Hyslop.
She is reported to have told directors of education at a private meeting in Dunkeld recently: "If a vote was to be taken in Parliament at the moment to take education out of local authority control, it would pass."
However, an attempt by the Convention of Scottish Local Authorities to placate Ms Hyslop and rescue the concordat over class sizes appears to have backfired: it led to accusations that the SNP's manifesto commitment to the 18-pupil limit had been ditched.
A "private and confidential" report to last week's meeting of the convention, which has been passed to The TESS, revealed that "a new way forward" was being proposed by Cosla's leadership, along with Ms Hyslop and John Swinney, the Finance Secretary - the two ministers who brokered the concordat.
This would be an attempt to counter the "corrosive effect" which negative publicity over the class-size policy was having on the concordat, the report stated.
Councillors backed the plan which will involve regular meetings between national and council officials to "provide reassurance" for Ms Hyslop on how much was being done, rather than accentuating how little could be achieved.
The Cosla paper continued: "This discussion would recognise that every council will be in a different situation and that the pace of pursuit of class size reduction (in P1-3) will vary from council to council.
"It will allow councils to outline very local considerations like the ability to pursue this policy in some parts of the council area but not in others, and innovative approaches to policy, such as the use of additional teachers within existing classes."
Tellingly, the new deal also involves a decoupling of the "contentious" aim of maintaining teacher numbers at the 2007 level of 53,000, while rolls fall, and class sizes. This "never was and cannot be a concordat commitment and should not be used as a proxy indicator of performance regarding class size reduction", the report claims.
Latest figures show that only 13 per cent of P1-3 pupils were in classes of 18 or fewer in 2008. But there has been a steady, if slow, improvement since 1997 when only 7 per cent were in such classes. The Government continues to stick to its line that it expects "year-on-year progress" towards the goal, depending on local circumstances.