Manchester United, Chelsea, Arsenal and Liverpool – the clubs who traditionally occupy the top four spots – are thought to have led objections to the proposal.
Premier League chairmen decided against examining its feasibility any further at their monthly meeting yesterday.
“The main topic of discussion was the Champions League play-off for that fourth qualifying place,” said Premier League chief executive Richard Scudamore.
“We gave a lot of discussion, a lot of detail, a lot of data. But there was not enough support to take the idea forward, so we won’t be discussing that proposal any further.”
The plan – which would take the Champions League place away from the fourth-placed team and hand it to the winner of a play-off between those finishing fourth to seventh – drew a mixed reaction when it was first suggested last month.
Managers from the so-called Big Four, who have occupied the top four spots in five of the past six seasons, criticised the idea for being unfair.
Everton boss David Moyes, whose team broke the cartel in 2005, also dismissed it, but Aston Villa’s Martin O’Neill voiced his approval.
The idea was to increase the unpredictability of the league, but West Ham chairman David Gold said practical constraints got in the way.
“It was just a physical thing, finding time in the calendar,” he said. “The clubs that would be involved in a play-off could also be involved in the FA Cup and Champions League, so it just could not be done.”