Premier League Chief Excutive Richard Masters had approached executives from Arsenal, Manchester United, Chelsea, Liverpool and Manchester City on Wednesday asking them to relinquish their positions on working groups, Sky Sports said.
Tottenham Hotspur are not represented on any of the Premier League's key committees.
It follows Tuesday's meeting of the 14 Premier League clubs not involved in the Super League who "unanimously and vigorously" rejected the plans for the competition.
Chelsea Chairman Bruce Buck sits on the Premier League's audit and remuneration committee, while Arsenal CEO Vinai Venkatesham and Manchester City CEO Ferran Soriano are members of the Club Strategic Advisory Group.
Manchester United executive vice chairman Ed Woodward and Liverpool chairman Tom Werner are part of the Club Broadcast Advisory Group.
The six Premier League teams that signed up for the venture withdrew on Tuesday following an intense backlash from fans, players and the British government alongside threats of bans and sanctions from the game's European and world governing bodies.
Spain's Atletico Madrid and Italy's Inter Milan pulled out on Wednesday, while AC Milan indicated they are also abandoning the project.
Juventus Chairman Andrea Agnelli said the conpetition cannot proceed any longer after the English teams pulled out but Real Madrid president Florentino Perez said the project was not dead.
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