A formal review has been commissioned by governing body SANZAAR but a recommended structure, with the input of broadcasters, is still months away.
This year's new four-conference system threw up multiple anomalies.
The Highlanders (52), Chiefs (51) and Crusaders (50) all finished with more points yet it was the Brumbies (43) who hosted a quarter-final in Canberra as the Australian Conference winners.
The Cape Town-based Stormers (51) hosted a quarter-final without having played a New Zealand side and still finished behind the Highlanders and Chiefs, who had to travel.
Riach and Lee are both convinced an overhaul should at least be discussed this week.
"The issue is the integrity of the competition when a team with significantly less points earns the right to host a quarter-final," Riach said.
"Canberra and Cape Town hosted for their clubs this year when more successful teams did not.
"It may be a hard one with broadcasters wanting a final in each time zone but a straight top eight would go a long way to solving the integrity issue."
Lee pressed the same point while also understanding the difficulties when the 18 teams are spread across five countries.
"You want all countries involved in finals but at the business end of the competition you want the best teams giving themselves the best chance," Lee said.
Lee pitched a straight 1-to-8 seeding for the quarter-finals or a more radical two-division, Australasia-South Africa concept with a dissolving of the pure Australian Conference.
This year, that would have rewarded the Hurricanes and Highlanders with home quarter-finals and the Crusaders and Brumbies with away games.
"If the Queensland Reds and NSW Waratahs are the two top teams, so be it, but my point is that more can be done to even it out in the quarters," Lee said.
Riach said he had read of informal discussion about the number of Australian and South African teams.
"It appears there is some talk around and it will probably flow into conversations this week," Raich said.
- news.com.au