The Jimmy Reid Foundation (JRF) and its spin-off the Common Weal project have been linked together but proposals to separate the initiatives have run into problems over a failure to agree a division of resources.
The relationship between JRF convener Bob Thomson and its ex-director Robin McAlpine, who has proposed winding up the Foundation, is said to have "completely broken down".
Jimmy Reid was the figurehead in the famous Upper Clyde Shipbuilders work-in staged in the early 1970s.
After he died in 2010, the JRF was set up as a non-partisan think tank to mark his legacy.
As JRF director McAlpine also created the Common Weal initiative, which looks at developing an alternative economic and social model for Scotland based on policies from the Nordic countries.
Thomson and McAlpine are understood to have had disagreements on the role and purpose of the JRF. The Foundation's governance structure has also added to the tensions.
Neither the JRF nor the Common Weal are companies in their own right, but came under the umbrella of Left Review Scotland Ltd.
As revealed recently by the Sunday Herald, there was an agreement in principle for McAlpine to leave the JRF and take charge of the Common Weal.
However, although McAlpine has left the Foundation, attempts to formalise the split broke down earlier this month in acrimonious circumstances.
It is understood Thomson, on behalf of the limited company's directors, proposed a transition agreement that would have given McAlpine and his staff cash until the end of the year.
Sources have told the Sunday Herald that McAlpine then tabled an alternative solution. He proposed that Left Review Scotland Ltd and the Foundation be wound up.
He also proposed that, once tax and other liabilities were settled, any resources be distributed between Common Weal and a new organisation he has offered to help set up to honour Reid's memory.
Neither plan is believed to have been agreed.
One insider said: "The relationship between Bob and Robin has completely broken down."
Tory MSP Murdo Fraser said: "These splits in the far Left are increasingly reminiscent of Monty Python's Judean People's Front [from the film The Life of Brian].
"If these groups cannot even agree among themselves how to organise, why on earth should anyone trust their vision of an independent socialist Scotland?"
McAlpine said: "Everyone involved with the Common Weal project is now working with and through Common Weal.
"We have many exciting plans for the future and we are full of hope that Scotland is on the cusp of real change."
Thomson declined to comment.