Edinburgh may well need to improve their league position to feature in the European Cup next season.
It is believed a Six Nations committee meeting in Paris on Monday agreed a structure to replace the Heineken Cup from September, if broadcasters Sky and BT can compromise over TV coverage.
The new tournament would have seven teams from the Pro12 in place of 10.
Edinburgh are currently eighth, although they have a game in hand on Newport Gwent Dragons.
That fixture is the postponed New Year's Day game with rivals Glasgow, who are currently fifth in the standings.
The new tournament - if ratified - will involve 20 teams in place of the current 24, with the top six from the English and French leagues qualifying automatically.
There will be seven teams from the Pro12, with one guaranteed representative from Ireland, Italy, Scotland and Wales with the other three places being decided on league position.
The 20th place in the tournament is likely to be decided by a two-leg play-off between the clubs that finish seventh in England and France.
Under the current qualifying arrangements two teams in Italy and Scotland have automatic entry to the Heineken Cup with 10 teams in total qualifying from the Pro12.
The future of the Heineken Cup has been in doubt since June 2012 when the top French and English clubs announced their intention to withdraw from the tournament once the current "accord" ran out at the end of the 2013-14 season.
They proposed their own competition, the Rugby Champions Cup, saying they were unhappy with the way teams qualified for the Heineken Cup and the distribution of cash generated by the tournament.
The English clubs in particular were dissatisfied with tournament organisers - European Rugby Cup Ltd (ERC).
BT paid £152m for rights to broadcast English club rugby including their participation in a European tournament - just weeks before ERC announced a new deal with Sky to cover the Heineken Cup.
There was also a rift between the four Welsh regions (Newport Gwent Dragons, Blues, Ospreys and Scarlets) and the Welsh Rugby Union - after the regions gave their support to the proposed breakaway Rugby Champions Cup.
Edinburgh finished third in Heineken Cup Pool 6 this season, winning three of their six matches, while Glasgow were bottom of Pool 2 with just two victories.