The loan, which would be directly to the government rather than to state utility Eskom, is "under discussion", Marie Francoise Marie-Nelly, the bank's director for South Africa, said in an interview in Marrakech, Morocco.
"It is going to come very soon," she added, declining to specify a timeframe.
South Africa is facing its worst power crisis, with Eskom's ageing, coal-fired plants often breaking down. Rolling power cuts have crimped economic growth, while fuelling private investment in renewable energy.
"It's a policy development loan which supports critical reforms," Marie-Nelly said of the potential World Bank funding. "There's a particular focus on transmission, because it is a stumbling block in terms of bringing new (capacity) that is going to be built mainly by the private sector."
In February, the South African government agreed to take on over 254 billion rand ($13.4 billion) of Eskom's debt through a debt relief scheme, subject to conditions.
The main condition was that the power utility would not be able to take on any new debt for three years unless approved by the country's finance minister.
In 2019, the government pledged to split Eskom into three subsidiaries - transmission, generation and distribution. Eskom said in August that its transmission arm would not be operational until 2025.
The World Bank loan would also support South Africa to make a "just transition" away from coal, to ensure vulnerable people do not suffer as a result, Marie-Nelly said.
She said the government was "also looking at the broader climate agenda, including looking at the carbon tax."
In November 2022, the World Bank approved $497 million in financing to decommission and repurpose one of Eskom's coal-fired power plants.
