The 12 founding members of the breakaway Super League are "ready for dialogue" with domestic leagues and UEFA.
Six Premier League sides, as well as three from Spain and Italy, announced on Sunday night that there were forming their own competition.
It has received widespread condemnation with UEFA's and FIFA's president both slamming the idea.
UEFA chief Aleksander Ceferin claimed the move was a "spit in the face of football lovers."
Prime Minister Boris Johnson and French President Emmanuel Macron have also come out to oppose of the idea.
But leading Super League figures are confident that talks can lead to a greater understanding of the proposals and halt some of the backlash, reports ESPN.
UEFA have threatened to ban players who represent clubs in the Super League from playing international football.
Premier League rules state that clubs can only play in competitions stated in rule L9 - and the breakaway competition is not one of them.
It means the six clubs could be axed from the top flight as they continue to pursue Super League plans.
A statement from the Premier League has said: "The Premier League, alongside The FA, met with clubs today to discuss the immediate implications of the Super League proposal.
"The 14 clubs at the meeting unanimously and vigorously rejected the plans for the competition.
"The Premier League is considering all actions available to prevent it from progressing, as well as holding those Shareholders involved to account under its rules.
"The League will continue to work with key stakeholders including fan groups, Government, UEFA, The FA, EFL, PFA and LMA to protect the best interests of the game and call on those clubs involved in the proposed competition to cease their involvement immediately. "
