Wales Online says the Durban-based Sharks are set to leave the competition to join the European PRO14 competition for 2019-20.
The Cheetahs and Kings, who were cut from the down-sized Super Rugby last year, already play in the competition which includes teams form Ireland, Italy, Scotland and Wales.
The report said that the Lions and Stormers would likely follow suit.
Despite the Lions making the Super Rugby final last year South Africa's franchises feel they are handicapped due to the different time zones.
But SANZAAR chief executive Andy Marinos has described the report as unfounded.
"SANZAAR - through its joint venture partners - Australia, Argentina, New Zealand and South Africa - is currently engaged in a detailed strategic planning process that will deliver a roadmap for the organisation, Super Rugby and The Rugby Championship from 2018-2030," he said.
"As part of this process the partners have fully committed to the strategy and future participation.
"Any talk of a change to the stakeholder relationship and partners withdrawing, and so-called Trans-Tasman competitions is unsubstantiated speculation and simply wrong."
South African rugby has also seen an exodus of top players who chase lucrative deals in Europe, with the move to the PRO14 considered a way of stopping that trend.
The Cheetahs finished third in their conference this season to make the play- offs, and PRO14 organisers believe the inclusion of further South African sides would increase the standard of the competition.
Last week a Fairfax report revealed that Super Rugby bosses were looking at expanding into the USA, which now appears to be a contingency plan should the South African franchises jump ship.