Councillor Miller made her comments as the Scottish Prison Service pressed ahead with moves to break with existing partnership arrangements with local government on key support services.
She said: 'I am concerned that steps being taken by the Scottish Prison Service could threaten key services.
'Councils currently provide social work prison services. The Prison Service wants to put those services out to tender. We believe it could be illegal for councils to do so. We have asked the Prison Service to talk to us about this. They have declined.
'The timing of Prison Services' actions is also unhelpful. The Scottish executive and local government are currently in the throes of reforming the way criminal justice social work services are delivered. The Prison Service's actions cut across that work.
'COSLA has already made its concerns plain to the Scottish executive. We will be raising the matter again with the Minister for Justice and asking him personally to intervene.'