Prominent clubs from those leagues intend to compete in the Rugby Champions' Cup instead, with the opporunity for Celtic and Italian clubs to join later.
The French Rugby Federation, however, have indicated it would not support such a venture and any Anglo-French breakaway tournament would require FFR and Rugby Football Union approval to go ahead.
Canadian lawyer Graeme Mew has been acting as an independent mediator in the dispute, although neither Premiership rugby nor their French counterparts intend to be present at the next round of negotiations on October 23.
Instead they have produced media packs to announce their proposed new competition. "The recent media releases from the LNR and Premiership Rugby lacked respect," said Lux. "I hope we will be able to reach an agreement. It would be disastrous to deprive players and fans of participating in such an outstanding tournament."