Europe's leading clubs have demanded a drastic cut in the number of international fixtures and a greater say in how the game is run.
The current calendar provides for 12 games a year but the European Club Association (ECA) wants a 50% cut.
"We would prefer six double dates over a two-year qualifying period," said ECA board member and Manchester United chief executive David Gill.
With the existing agreement running out in 2014, Fifa has proposed 17 games.
That proposal provoked fury from Europe's top clubs when it emerged last year.
Gill, who also sits on the Football Association board, said the clubs were determined to trim international fixtures and that the "single date" friendlies in June and August should be the first to go.
Last month England's friendly against the Netherlands was called off because of riots in London but the summer friendlies remain a bone of contention with the clubs, particularly in southern Europe, where league football starts towards the end of August.
Karl-Heinz Rummenigge - Gill's counterpart at Bayern Munich and the ECA president - went further than the United chief executive, describing the summer friendlies as "nonsense".
"They are added to make money, nothing else. It's got to stop," said Rummenigge. "The clubs are the most important stakeholders in football - without us you have no business - and yet we have no voice."
Rummenigge has been outspoken in his criticism of Fifa and Uefa in recent months but was more conciliatory in Geneva.
"Our goal is not to break away - we know we have to release our players to the international teams - but we want good governance, democracy and transparency," he said.
The former Bayern, Inter and Germany star claimed the clubs had agreed to ditch the second group stage of the Champions League in 2004, in order to give the players more rest, but those dates have been filled by international games.
"When I played in the 1980s, for example, only eight teams made the European Championship finals, now it is 16 and in 2016 [in France] it will be 24. So it has tripled," added Rummenigge.
"It is the same with the World Cup: it was 16 teams, now it is 32. And then you have the qualifying games too."
The plan proposed by the ECA - the successor body to the G-14 group which represented Europe's most powerful clubs - would see the European World Cup qualifying phase reduced to 13 groups of four, with only the winners progressing.
The clubs are also furious about what they see as the pittance they receive in compensation for releasing players to compete in international competitions.
The issue of insurance is also a long-standing complaint, with England being an exception in providing cover to clubs for players injured on international duty.
The most recent World Cup in South Africa produced revenues for Fifa of $3.7bn (£2.3bn) but only $40m (£25m) was passed on to the clubs. This works out at about $100,000 (£63,000) per club: a small price, they say, for providing the talent.
ECA board member and AC Milan director Umberto Gandini pointed out that Uefa is selling the TV rights for the European Championships on a central basis.
And he suggested the clubs should be given a percentage, as opposed to the capped amount they have been receiving. Uefa itself takes 25% of the Champions League money, Gandini observed.
Rummenigge revealed he met Fifa president Sepp Blatter and Uefa boss Michel Platini separately in Zurich last month and discussed the ECA calls for fewer games and more money.
He said he was "not pessimistic" that a deal could be reached and added that Platini was especially keen to compromise.