The strike, now in its third week, has affected coal exports in one of the world's biggest suppliers of the power station feedstock, and may impact the country's target of exporting 65 million tonnes this year.
The transport strike has also dented exports of metals, cars, fruit and wine to Europe and Asia, as well as imports of vehicle parts and fuel and cost the economy at least 7 billion rand (£630 million) in lost production and sales.
The South African Transport and Allied Workers Union (Satawu) said its members appeared to favour the new offer from Transnet, with a final vote expected later on Thursday.
"We are quite positive. When we speak to our members, everyone believes that we will have a deal," Satawu President Ezrom Mabyana told Reuters.
Transnet said the new offer, which includes a once-off payment to all bargaining sector employees, was a "breakthrough" which could end the strike.
The ruling African National Congress (ANC) has pressed both sides for a quick solution, warning the dispute could hurt the World Cup, which starts on June 11th and runs for a month.
Satawu, which represents 39 percent of Transnet's 54,000 workers, has called for sympathy stoppages at other transport firms countrywide, including at the national airline and the coal export terminal, which could start next Tuesday if the dispute with Transnet is not resolved.
Recent strikes have drawn criticism from economists and the central bank who say unions are trying to hold the government and state enterprises to ransom by staging strikes close to the World Cup, to squeeze pay hikes above inflation of 5.1 percent.
Late on Tuesday, South Africa's biggest union called off a strike at power utility Eskom due to start on Wednesday after the state-owned firm obtained a last-minute court order declaring the planned industrial action illegal.
BILLION LOSSES
With a backlog that will take at least a month to clear, the strike has taken its toll on the country's mining, transport and manufacturing industries and hurt producers of perishable goods.
Transnet said that with 65 percent of its workers back at work after the company's bigger union accepted a previous wage offer, the logistics group had managed to move a backlog of crucial shipments, including World Cup cargo.
Shipping companies are asking clients to pay a surcharge to partly recover their losses. Fruit producers began using costly air freight to export their produce and car manufactures have opted to fly in some parts to be able to keep production going.
All automotive plants were limping along due to the backlog at ports, an industry body said.
Fuel imports through South Africa to landlocked Botswana have fallen by a half, but supplies within South Africa itself have been unaffected.
Analysts said the strike is likely to have long-lasting consequences on the country's exports, with South Africa losing some contracts to other markets such as India or Brazil. Retrenchments may also be loom
