The Cheetahs and Kings — discarded from Super Rugby — compete in the PRO14, which includes teams from Ireland, Italy, Scotland and Wales.
The Sharks are named as the first team "likely to commit" with the Lions and Stormers next in line.
The story states: "PRO14 bosses have been heartened by the on-field impact of the Cheetahs and Kings and believe the prospective introduction of the Sharks and further South African sides will significantly increase the quality of the competition and make it more attractive to broadcasters and investors.
"Under (CEO Martin) Anaya, the PRO14's TV income has risen from £12m to somewhere in the region of between £20m and £30m with a new broadcasting deal seeing paid-for provider Premier Sports taking over the rights for next season. The imminent introduction of further South African sides has been factored into that three-year contract.
"South African rugby has seen its top players leave left, right and centre for lucrative moves to Europe in recent years and it is hoped moving teams to the PRO14 can help stop that trend."
It is estimated the Cheetahs and Kings brought about $1m each to the competition.