Munster won the Heineken Cup in 2006
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The future of the Heineken Cup depends on English clubs agreeing a deal with the Rugby Football Union.
Talks between the two parties are expected to resume on Thursday, with a deadline of 18 May set for them to come up with a workable agreement.
The major problem to be resolved is the management of England's elite players.
"The biggest issue is going to be money - what it's going to cost the Union and can the Union afford it," said RFU chief executive Francis Baron.
The cost of compensating the clubs for sacrificing their England players for longer periods has been estimated at between £12m and £17m.
Baron added: "These are very big numbers and we don't have the resources to meet the demands. That will be the crux of the discussions.
"The issue is going to be how we can structure a deal which gives the clubs financial funding to compensate them for what they are delivering.
"If we have to lose funding from the community game to the elite game all we would have is a new set of problems."
RFU chairman Martyn Thomas warned: "We cannot compromise on what we need to deliver for the England team.
"If we cannot get a deal (director of elite rugby) Rob Andrew feels he needs to deliver for England then there will not be a deal."
French Federation boss Bernard Lapasset said he was cautiously optimistic about the future of the tournament.
"We are very close to finalising it but there is no agreement yet between the RFU and (English clubs' body) Premier Rugby Ltd (PRL)," said Lapasset.
"But they are hoping to find a solution soon, it's encouraging."
But a provisional agreement about the tournament's future emerged after a meeting in Dublin on Tuesday.
The statement after the meeting in Dublin made it clear that the sticking point to the future of the tournament was the impasse between PRL and the RFU.
"All parties reaffirmed their commitment to the long-term future of the Heineken Cup and European Challenge Cup and to providing a stable future for both ERC tournaments," said the statement.
"The parties reached a conditional agreement which, on completion of discussions between RFU and PRL over the next two weeks, will ensure the long-term future of both European tournaments and the participation of the leading teams from all six competing nations."
The row began when the PRL claimed the RFU turned its back on a deal to give them a stakeholding in the European competitions.
The top French clubs threatened to boycott the event as a result and the English clubs said they would follow suit.
But the RFU insisted that no such deal had been struck and said a boycott would be regarded as a termination of an agreement it has with PRL.