The English clubs have been frustrated by the lack of progress made on the future shape of European rugby in two lengthy stakeholder meetings, held in Dublin and Rome.
A third meeting, held last week in Paris without Premiership Rugby, saw the French clubs reject two different proposals for new-look competitions tabled by the Rabodirect PRO12 clubs.
Angry Premiership Rugby officials interpreted that meeting as an attempt to drive a wedge between the English clubs and their French allies.
Premiership Rugby decided not to pull out of Tuesday's meeting - but they will press for a new approach in the hope of bridging an impasse which threatens the future of the Heineken Cup.
Premiership Rugby want to kick-start the negotiations because they believe a solution needs to be found as a matter of urgency, potentially by the end of the year.
The English and French proposal is for the PRO12 clubs to qualify for the Heineken Cup on merit - rather than be guaranteed places - and for the money to be divided equally between the three leagues.
The Anglo-French plan would see the Heineken Cup trimmed to 20 teams with four clubs dropping into a strengthened Amlin Challenge Cup. There would also be a third tournament created for clubs in developing nations.
The proposal is underpinned by a television deal with BT, which is worth up to £100million. Premiership Rugby argue all competing nations would be better off under their plan.
The PRO12 clubs currently receive 52% of the income, with the English and French clubs taking 24% each.
But the Celtic nations and Italy have so far been staunchly opposed to relinquishing their automatic entry into the Heineken Cup, even if they end up earning more money.
All the stakeholders are due back in Dublin on Tuesday but Premiership Rugby believe having 17 different people sitting around a table is not working.
One option Premiership Rugby has considered is whether the negotiations should be conducted by a much smaller group.
The Rugby Football Union has been supportive of Premiership Rugby's position and they could have a key role to play in brokering a solution.
The RFU and Six Nations chairman Bill Beaumont has already offered his help in that regard. Chief executive Ian Ritchie and professional rugby director Rob Andrew were both at the meeting on Wednesday.
Premiership Rugby want action to kick-start the negotiations because they believe a solution needs to be found as a matter of urgency, potentially by the end of the year.
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