Changes in 2003 led to more knockout ties but fewer games overall and G14, representing 18 of Europe's leading clubs, wants a rethink.
"We are not talking about doubling the number of games, it may be adding just one or two," Barcelona vice-president Ferran Soriano told BBC Sport.
Although the 2003 changes have been broadly welcomed, Europe's top clubs were furious that when the format change was initially proposed in 2002 they were not consulted.
The new format ensured that teams played 12 games instead of 16 to reach the final.
"We also want to guarantee competition in every game - in some of the final group games there is no real competition because the first and second place is already decided," added Soriano.
G14 wants the format change in place by 2009 at the latest - but preferably for the start of the 2008 season.
Last week G14 released a 10-point plan seeking a direct vote for clubs in Uefa and for the organisation to be included when the international calendar was agreed.
