Eddie Jones thinks it shouldn't happen, New Zealand insists it can't happen, and tournament organisers say there's no sign of it happening.
The possibility of the European Six Nations rugby tournament expanding to include world champions South Africa would be the most stunning development in the sport in years, a game-changer for both the northern and southern hemispheres.
British newspaper The Daily Mail reported on Saturday that negotiations have taken place that will lead to the Springboks joining a new championship in 2024.
It would contain seven nations, with England, Wales, Scotland, Ireland, France and Italy already competing.
It would also mean South Africa leaving the four-nation Rugby Championship in the southern hemisphere, which also includes Australia, New Zealand and Argentina.
World Rugby, the sport's governing body, said it would not be commenting on the reports, but others are.
Mark Robinson, the recently hired chief executive of New Zealand Rugby, said the Springboks are committed to being part of Sanzaar - the body that oversees the Rugby Championship and Super Rugby - until 2025.
"We're very comfortable in our relationship and South Africa's relationship with Sanzaar," Robinson was quoted as telling Radio Sport in New Zealand.
"They are people that we trust, they are very honest and they've been great partners over the last 25 years. We would like to think that we would be privy to those sorts of comments or conversations if they had been had."
Tournament organisers have also played down the reports, saying the Six Nations Council "has had no discussions regarding South Africa's inclusion" in the competition.
Meanwhile, England coach Jones has advised against any tinkering of the format of what he called "the greatest rugby tournament in the world."
"Why would you want to add other teams that are going to decrease the level of competition," the Australian said, using the expansion of Super Rugby from 12 teams to its current number of 15 as a cautionary tale.
"I can only talk from experience," Jones added.
"Super Rugby was the golden egg of rugby - brilliant, 12 teams, competitive. As soon as it had gone to 14 and 15, it had lost its allure."
Jones said what makes the Six Nations so special is "the history of the relationships between the nations."
"Someone was giving me a history lesson on Scotland and the number of different things that have happened in the rivalry with England," he said. "So there's a lot of meaning to a lot of people for a game like this.
"You want the best teams playing against each other. There's something about the Six Nations - because of the history of the relationships between the nations, it makes it more outstanding.
"The competition is much harder contested than the World Cup. It's become a lot more physical and it's only going to get more so.
"You don't want this type of game every week, but southern hemisphere coaches certainly admire the Six Nations.
"From the first Six Nations I did to now, I think we've seen a general rise in the quality of the teams."