This move is said to be on a "broadcasters' wishlist".
This list also proposes a revamped Rugby Championship with mini tours which include midweek games for the international teams against Super Rugby sides.
This would help make up for the shortfall - estimated at $7m in Australia — created by the departure of Japan's Sunwolves from Super Rugby.
The presentation to SANZAAR was made by New Zealand's Sky Sport plus Fox Sports (Australia), Super Sport (South Africa) and Sky Sports (UK) a month ago.
The broadcasters also want cities and regions to be in the team names.
The newspaper report says SANZAAR is forging ahead with a plan B in case World Rugby's embattled campaign to start a global competition falls over.
The proposals include enabling some elite players to sign for Super Rugby teams from other countries without this hampering their test status.
This raises the possibility of a superstar All Black like Brodie Retallick playing for say the New South Wales Waratahs and remaining in the test side, a concept which is standard practice in many sports but outlawed by New Zealand Rugby's residential rule.
"The 'marquee player' concept is effectively proposing a safe zone for the movement of players, allowing them to move overseas but to countries in the same competition, meaning no schedule clashes and a closer high performance relationship," the SMH report states.
"Having Australians playing in South African teams, for instance, could also help boost interest in the traditionally poorly-watched games between South African and Australian teams."
"Themed rounds" and "consistent time slots in each nation" are also proposed, although without explanation.