It added that it had received a non-resolution notice from the Commission for Conciliation, Mediation and Arbitration (CCMA).
Asked if Num members at Eskom would now strike, spokesperson Lesiba Seshoka said the members would make that decision.
"Eskom can argue as much as it likes that it is an essential service and therefore the strike would be illegal - if our members want strike action there's going to be chaos," Seshoka added.
On Monday evening Eskom had made a wage increase offer of 8%.
In addition, the company also offered a 5.6% increase on certain allowances as well as a payout of R12 000 to all employees in two equal instalments.
Trade unions, however, rejected the offer.
Num together with Solidarity and the National Union of Metalworkers of SA (Numsa) were demanding a 9% increase and a housing allowance of R4 000 per month.
"Personally I had expected a revised offer of 9% with no housing allowance," Seshoka said.
Meanwhile Eskom told Sapa that it was aware that a notice of non-resolution had been issued by the CCMA.
"We had planned to take the commissioner through our revised offer around 1pm today.
"We went to meet him at the Killarney Mall and we were told he was in a meeting," Eskom's head of human resources Bhabhalazi Bulanga said.
He added, however, that the issuance of the non-resolution notice by the CCMA did not preclude Eskom from holding further discussions with the trade unions.
"We hope to still meet the unions later today at around 4pm."
Bulanga claimed that Eskom had revised its offer and wanted the unions to be aware of the details.
- Sapa