EPFL chairman Lars-Christer Olsson said he wanted more teams from the biggest leagues to play their way through the qualifying competition instead.
European football body UEFA last year announced that it would give more slots to teams from the four biggest leagues, effectively England, Spain, Germany and Italy, while cutting those allocated to sides from smaller countries.
Those changes will come into effect for the 2018-21 cycle but Olsson told reporters he was already looking ahead to 2021-24 when he was hoping to persuade UEFA to do an about-turn.
"There is a common view among the leagues that there should be less clubs directly qualified (for the group stage) because qualification for the Champions League should mean more and give more opportunities for more teams to qualify," he said.
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The Swede added that the format to be introduced next year would "widen the gap between the rich ones and those who have less".
Olsson was speaking after EPFL reached an agreement with UEFA which would guarantee it a part in future decision-making on matters like competition structure and match scheduling.
Olsson said that UEFA President Aleksander Ceferin, elected last year, is "obviously looking for a bigger inclusion of stakeholders than in the past and we have a totally different climate now".
He said both parties had agreed about the dangers of a handful of clubs dominating European competition.
"We have agreed that we are both going to work to develop and enhance the competitive balance, including in domestic competitions," he said. "We are convinced that keeping competitive balance is necessary to keep the interest of the fans and make competitions more interesting."
Olsson said that there was no chance of Champions League knockout stage matches being played on Saturday nights instead of midweek, which French media reports said last week had been proposed by some clubs.
"As far as I can understand, the international club matches should be played in midweek apart form the final."
(Writing by Brian Homewood in Berne editing by Mark Heinrich)
