It was announced in April that Super Rugby would be trimmed from 18 teams to 15 going forward, with two of the South African representatives set for the chop.
That move will leave South Africa with four sides in the southern hemisphere competition, while Australia will also see one of its teams cut.
The Cheetahs and Southern Kings are widely expected to be the sides that lose their place, but the definite identity of the teams at risk remains unclear.
The South African Rugby Union announced on Wednesday that a special general meeting will be held on July 7 to determine "the SA teams to participate in Super Rugby".
Chief executive Jurie Roux confirmed a decision would be made using a proposal from SA Rugby's executive council and the franchise committee, which is made up of the six current teams.
The proposal will also be discussed by a non-franchise committee ahead of the meeting, that panel containing representatives from South Africa's 14 provincial rugby unions.