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.