They have also called for the removal of public enterprises minister Pravin Gordhan.
Numsa spokesperson Phakamile Hlubi-Majola said they "reject the privatisation and unbubdling of Eskom... we reject the fact that they have introduced the likes of Andre de Ruyter who has no ability to run this SOE.
"This also applies to the minister, we demand that Pravin Gordhan be removed."
The EFF has called for Gordhan to be fired, threatening to disrupt the state of the nation address (Sona) if he is not.
Gordhan's ability to resolve the Eskom and energy crisis has been brought into sharp focus after ongoing power cuts and general instability at the power utility.
The resignation of Eskom's board chairperson, Jabu Mabuza, appears to have been the final nail on the coffin, prompting various stakeholders to demand the government finds a permanent solution to the country's energy crisis.