Zaldivar workers will vote on whether or not to strike by the end of the week, legal advisor Marcos Lopez, who was also employed by a union at BHP Billiton's Escondida mine during a historic 43-day strike earlier in the year, said.
Meanwhile supervisors at Centinela mine have already voted to strike although they expect a government mediation mechanism to extend negotiations for at least five more days, a spokesman for Chile's mining federation said. The federation represents workers at some of Chile's biggest mines.
The combined annual production at both mines is 160,000 tonnes of copper. Chile is the world's largest producer of the red metal.
Antofagasta said in an e-mail to Reuters that talks were continuing and following normal deadlines, without commenting specifically on the potential strikes.