Heineken has backed the event since 1996, spending an estimated £4m a season on it. In 2005, it renewed its deal with European Rugby Cup for a further four years, but earlier this year, French clubs said they would boycott the event, accusing the French Rugby Federation of reneging on a deal that would have handed them a 50% share in ownership of the tournament.
Their English counterparts are now insisting on a similar deal.
The clubs' withdrawal could see the tournament postponed for a year, although it has been suggested that it could feature teams from Ireland, Scotland, Wales and Italy.
Mike Parker, director at Velocity Sports & Entertainment, believes the event will lose its appeal without the participation of English and French clubs. 'If the Heineken Cup gets watered down it risks becoming akin to (second-tier competition) the European Challenge Cup,' he said.
A Heineken spokesman conceded that while the parties involved have expressed the desire to see a tournament, 'how it pans out is outside of our control'.