This could bring an end to the country's longest and costliest strike which started five months ago.
Members of the Association of Mineworkers and Construction Union (AMCU) will meet in the mining town of Rustenburg northwest of Johannesburg, where they will be updated on wage talks, the union's president Joseph Mathunjwa told Reuters.
In a series of mass meetings in early June, union members accepted the wage offer "in principle", while introducing new demands that producers have said were "unaffordable".
About 70,000 AMCU members downed tools in January at mines run by Anglo American Platinum, Impala Platinum and Lonmin to demand that their basic wages be more than doubled to 12,500 rand ($1,200) a month.
"We met Thursday and Friday in marathon sessions and my sense was that those discussions were fruitful. The last hurdle is always difficult and sensitive," Implats spokesman Johan Theron told Reuters.
Marred at times by violence, the strike has hit 40 percent of global production of the precious metal used for emissions capping catalytic converters in automobiles.
The stoppage dragged Africa's most advanced economy into contraction in the first quarter and has so far cost the companies almost 24 billion rand ($2.25 billion)in lost revenue, according to an online tally run by the three firms.