Liverpool won the 2018-19 Champions League
The revolutionary changes to European football planned for 2024 are likely to either be delayed or scrapped.
Uefa was proposing a Champions League containing four groups of eight clubs, as opposed to the current eight groups of four, meaning 14 games, some of which could be played at weekends.
The proposals came after pressure from leagues below the "big five" - England, Spain, Italy, Germany and France.
However, after months of talks, no overall consensus has been reached.
Promotion and relegation from the Europa League and the new Europa League 2, a third club competition which starts in 2021, had also been suggested as a way of ensuring a rotation of clubs, to prevent the Champions League appearing to become a sealed competition.
Ajax chief executive Edwin van der Sar has been among the most vocal demanding change, pointing out the present qualification system could have led to his club having no European football at all after August, even though they came within seconds of getting to last season's Champions League final before Lucas Moura's dramatic injury-time goal for Tottenham in Amsterdam.
While the clubs remain committed to change, the likelihood is that anything implemented by 2024 will be much less radical than initially envisaged.
Ex-Netherlands goalkeeper Van der Sar was present in Geneva on Monday for the first day of a two-day meeting of Europe's leading clubs, where England's "big six" clubs - Manchester City, Liverpool, Chelsea, Tottenham, Arsenal and Manchester United - were also represented.
Sources have said resolving the Ajax "issue" is relatively straightforward and could be achieved by allowing all semi-finalists into the group phase and introducing a play-off for the fourth-placed teams in the two lowest-ranking leagues who get four automatic group phase slots - currently Italy and Germany.
A far greater obstacle to implementing the proposed changes is concern among the major leagues, including the Premier League, that if Uefa's plan results in greater television revenue for their competitions, it will come at the expense of their domestic competitions.
There is disagreement about this, but the view is widely held and puts clubs in those competitions at loggerheads with counterparts in the Netherlands, Portugal, Belgium and Scotland, amongst others, where big-name clubs are restricted in their ability to progress because access to TV money from their own domestic competitions is strictly limited.
They feel unless action is taken quickly, the gap will end up being so wide, it will never be bridged.
Last season, the Premier League's bottom club, Huddersfield, earned £96.6m in TV money alone. In 2018, Scottish champions Celtic's overall income, including prize money from the Champions League, was £101.6m, a sum that was reduced markedly in 2019 because of their failure to qualify for the group stages of Europe's elite competition.
It is the lack of consensus which led to Uefa president Aleksander Ceferin cancelling the key tri-party discussions (involving Uefa, the leagues and the clubs) that were due to be held in Switzerland on Wednesday.
These talks have been put back indefinitely, with chances being that they may not be held until the end of the season.
Source: bbc.com