Rousseff told Argentine Economy Minister Sergio Massa that the bank's board of directors formally authorized a vote on Argentina's admission to the bank at the next meeting, the media reported.
The proposal, put forward by Brazil, will be discussed at the next meeting of the board of directors in the first half of August in South Africa, the report said.
The NDB is an international financial institution established in 2014 at the annual summit.
The NDB aims to mobilize resources for infrastructure and sustainable development projects in BRICS and other emerging markets and developing countries through the provision of loans, guarantees, and other financial instruments.
BRICS unites the world's largest developing economies — Brazil, Russia, India, China, and South Africa.
Several other countries intend to join the economic bloc, including Argentina, Iran, Indonesia, Turkey, Saudi Arabia, and Egypt. South Africa, which assumed the rotating BRICS presidency in January, will host the 15th BRICS summit in August.