The leading clubs of England and France have grown frustrated at the impasse in their negotiations with European Rugby Cup over changes to the format of the elite competition.
The clubs - who served notice to leave the ERC competitions, which include the second-tier Amlin Challenge Cup, last year - now intend to create rival tournaments.
They say clubs from other countries will be welcome to enter what will be 20-team events.
They have not ruled out reaching an agreement with ERC, but say they will not return to discussions unless there is tangible evidence their concerns are being met.
The English and French want changes to the structure of both continental competitions, principally over the number of teams involved, the qualifying process and how funds are distributed.
Mark McCafferty, chief executive of the English clubs' representative body Premiership Rugby, said: "We have had 15 months of discussions which haven't produced an outcome.
"There hasn't been a meeting since May and there has been no urgency over the summer.
"Our clubs have been very strong in saying they need clarity.
"If we can't reach an outcome involving all the European clubs, we at least have to set up a competition involving the English and French clubs.
"If others want to come into that competition then we can look at that but we have to get on and prepare."
The Heineken Cup has been highly successful since introduced in 1995-96 and its demise would be unpopular.
Yet as that could cut off a strong source of income for clubs of the RaboDirect PRO12 - the cross-border competition for the Celtic nations and Italy - there could be fresh desire to find a solution.
One of the prime concerns of the English and French is that they believe PRO12 clubs have an unfair advantage in terms of qualification.
For example, Scotland and Italy are guaranteed two Heineken Cup entrants, even if they finish in lowly positions in the PRO12.
McCafferty said: "Our view is that the competition is not a truly elite one as you don't have the 24 best clubs in there.
"There are a whole series of issues we have been through for several years with them that we feel need to be changed to make the competition stronger for everyone."
ERC has said the matter will be discussed at Wednesday's scheduled board meeting, which is due to be attended by Peter Wheeler of Premiership Rugby and Rene Bouscatel of French equivalent Ligue Nationale de Rugby.
A statement from ERC read: "While there is a shared sense of frustration among ERC's stakeholders at the lack of progress towards a new accord, the meeting will provide an opportunity for the parties to review the consultation process to date."