Spain's biggest two clubs and Italian outfit Juve are the only three remaining of the 12 European giants who signed up for the controversial project, with all others having withdrawn just days after the competition was announced last month.
UEFA, earlier this month, stated that Manchester United, Liverpool, Manchester City, Tottenham, Arsenal, Chelsea, Milan, Inter Milan and Atletico Madrid would not face Champions League or Europa League bans after pulling out of the proposed Super League.
The governing body warned that the three remaining rebel clubs could be sanctioned due to their unwavering stance.
UEFA stated: "UEFA has reserved all rights to take whatever action it deems appropriate against those clubs that have so far refused to renounce the so-called 'Super League'. The matter will promptly be referred to the competent UEFA disciplinary bodies."
Barca, Madrid and Juve responded by releasing a joint statement describing UEFA's threats of sanctions as "intolerable" and "unacceptable."
The three clubs defended the Super League proposal by stating that "structural reforms are vital to ensure our sport remains appealing and survives in the long-term".
They added that the founding clubs agreed that the new competition would only take place if it was "recognised by UEFA and/or FIFA or if, in accordance with applicable laws and regulations, it was deemed to be a competition duly compatible for all purposes with the continuity of the founding clubs in their respective domestic competitions".
Juve, Barca and Madrid claim the Super League provided "a unique opportunity to offer fans around the world the best possible show and to reinforce global interest in the sport".
The trio of clubs say they are "ready to reconsider the proposed approach" but it would be "highly irresponsible" if they abandoned a mission to "provide effective and sustainable answers to the existential questions that threaten the football industry".