Cosatu has vehemently opposed Ramaphosa's announcement that Eskom would be unbundled into three entities comprising generation, transmission and distribution.
"We remain totally opposed to any restructuring plan that will benefit the capitalist class and increase prices for the working class," Cosatu said.
Speaking to the Sunday Times on Friday, Ramaphosa said he was ready to have a "real heart-to-heart discussion" with labour so that they could all be on the same page.
But he appeared firm on one thing: inputs made during talks had to be "solution orientated".
"[We must discuss] how do we solve the financial crises, the issues of operational difficulties and how to avoid having all our eggs in one basket that comes with huge risk," Ramaphosa said.
Cosatu said both parties agreed to meet again after its upcoming central executive committee meeting set for next week.