The southern hemisphere championship between Australia, New Zealand and South Africa was launched in 1996 and later expanded to include Argentina.
But with the landscape of world rugby soon to change it could be either downgraded to a single round of competition or culled, South African Rugby Union chief executive officer Rian Oberholzer told reporters.
New Zealand and South Africa are planning bilateral tours, starting in 2026 when the All Blacks will visit South Africa for eight weeks, including four Tests and clashes against the provincial franchises, to be dubbed "The Greatest Rivalry".
One of the four Tests might be staged in a neutral venue like Twickenham in London, where the All Blacks and Springboks met on the eve of last year's Rugby World Cup in a lucrative crowd puller, or in the US where the Kiwis played last month against Fiji.
"People might think it's arrogant, but we think it's the greatest rivalry in rugby. The concept must be finalised and then we can get onto discussing commercial rights and broadcast deals," Oberholzer briefed local media this week.
South Africa will undertake a similar tour of New Zealand in 2030, which would look to mirror the success of the British & Irish Lions tours, held every four years and alternating between Australia, New Zealand and South Africa.
Oberholzer said South Africa were also committed to playing at least one Test annually against each of Argentina and Australia.
Last year it was announced that a new competition between tier one nations from the northern and southern hemispheres would be played every other year from 2026 in a shake up for the international game.
A "World League" has been mooted for some time to try to extract more revenue from the international windows and bring context to what have been friendly fixtures played traditionally in the southern hemisphere in July and in the north in November.
Six Nations sides England, France, Ireland, Italy, Scotland and Wales would be in the northern conference, with Australia, Argentina, New Zealand and South Africa in the southern conference along with two invited guests, one of which is likely to be Japan.
Teams from the north would travel south for three tests in July and then host three more games in November. A final would be played between the two first-placed finishers in each conference.
