Organisers of the Heineken Cup believe it would be "almost unthinkable" not to have English clubs in a European tournament.
There is uncertainty over Europe's biggest club competition's future as its current format comes to an end in 2014.
English clubs, and their French counterparts, are currently unhappy at qualification criteria and scheduling of the tournament.
The English teams are upset that Celtic outfits can rest their players for domestic games as unlike in England, there is no relegation or promotion in the PRO12 league.
This unhappiness between the English teams and their European counterparts has led to fears that Aviva Premiership sides will have to leave the Heineken Cup and form their own competition.
Premiership Rugby Limited (PRL), the organisation representing England's leading clubs, also announced that they had agreed a £152million deal with BT to show domestic and European matches from 2014 onwards.
That conflicts with another agreement between European Rugby Cup Ltd (ERC), the organisers of both the Heineken and Amlin Challenge Cups, and their existing UK broadcast partner Sky Sports.
The two factions held a meeting in Dublin last week but could not reach an agreement and another is scheduled to take place next Monday in Rome.
ERC CEO Derek McGrath has hinted that European rugby's governing body would be open to some sort of compromise to prevent the English clubs from withdrawing from European competitions.
"It is almost unthinkable that could happen," he said.
"I think everyone knows how important the tournament has become in every single country.
"It (having English teams pull out) is not something we are focused on in any way.
"We have a two-year notice period for a reason, which is to allow us to understand where we might be going to. That is an open opportunity to allow people to understand what we might do differently."
The ERC insisted PRL do not have the authority to agree TV deals for tournaments that are played outside their borders and McGrath criticised the PRL for thinking that all the clubs involved would agree with their proposal.
"There was a lot of surprise and there continues to be in terms of the decision to pre-judge an outcome," he said.
"We have a centralised approach to marketing. That is what all the unions have approved and that's what is recognised under the International Rugby Board (IRB) regulations so to do things in a different way is not only pre-judging an outcome, it's also doing it outside the institutions that are set down and respected by everyone.
"While there have always been challenges, there always has been respect for each other's country and cultures, etc. This has changed the agenda."
But the PRL are adamant they were allowed to negotiate their own contract as part of a deal they currently have with the Rugby Football Union (RFU).
The RFU themselves are investigating PRL's claim, but McGrath believes they do not have the RFU's permission to negotiate a separate deal.
"The board can only reject a deal that is not receiving the authority of (the country's respective) union under IRB regulations," he revealed.
"We understand that no approval was sought so therefore the ERC, even if it wanted to, couldn't recognise any such dealing."