But one South African writer has warned of the dangers, saying the country would be throwing its lot in with a second rate rugby tournament.
Rapport is reporting that the Lions, Bulls, Stormers and Sharks could join Europe's PRO14 by next year, or 2023 at the latest.
The Cheetahs and Kings, dumped by Super Rugby, have already joined the competition involving leading clubs from Ireland, Wales, Scotland and Italy.
According to Rapport, there is only room for five South African sides meaning one would miss out on a PRO14 place.
Rival media outlet Sport24 reported: "With Super Rugby 2020 suspended (because of coronavirus), this has been an opportunity for Sanzaar to reflect and while the message out of the organization has presented a united front, the mumblings of South African franchises cashing in for potentially more lucrative fees in Europe has only gathered momentum."
Sport24's chief writer Rob Houwing said the Covid-19 crisis, has "increased the ripples over South Africa's future in (Super Rugby) when it is increasingly struggling for the credibility of old anyway."
But Houwing sounded a warning.
"Naturally there will be travel, time-zone and some financially-related pluses to such a shift. You have to wonder, too, just how sustainable an all-Australasian Super Rugby would be, minus the obvious South African clout," he wrote.
"The considerable snag with PRO14, as I see it, is that it is in many ways only the 'best of the rest' in a UK/European context, given that English clubs continue to campaign in the almost certainly still more blue-chip, England-specific premiership.
"There are some extremely prestigious Irish and Welsh clubs and players, for example, active in the PRO14.
"But without the cream of English (and French) teams, PRO14 is just another tournament which can't even be described as the premiers barometer, unlike Super Rugby in the south."