The unions have been in negotiations since April with the utility, which is implementing the worst power cuts on record and has been mired in financial crisis for years.
Eskom said in a statement it had raised its offer to a final one of 5.25%, up from an earlier offer of 4.5% and an initial proposal of 3.75%.
The unions want wage hikes of between 9.5% and 12%.
NUM and Numsa had initially demanded a 15% increase in wages while Solidarity sought 10.1%.
"We rejected the proposal (Eskom's latest offer) because we feel that Eskom can do better. Food inflation is extremely high, and the cost of fuel and basic goods has skyrocketed," Numsa said in a statement.
"And to make matters worse, the South African Reserve Bank has hiked interest rates, which means our members are going to struggle even more to make ends meet."
The Sarb raised its main interest rate on Thursday to a 14-year high, a move the bank's governor described as "bitter medicine" needed to tame inflation.
Eskom and unions will hold a fourth round of negotiations on 13 and 14 June.
"Eskom is hopeful that it and the labour unions will find each other for the benefit of the company and in the best interest of the country," it said.
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