Documents reported by the Financial Times show the Spanish club believe they missed out on around 4.5 billion euros in revenue since UEFA blocked the breakaway project in 2021, including matchday, broadcast, and commercial income.
The move follows a Madrid court ruling that upheld a previous decision finding UEFA guilty of abusing its dominant position by stopping the Super League.
Real Madrid said the judgment "confirms that UEFA seriously breached EU competition law" and opens the way for "substantial claims" for compensation.
UEFA, however, have insisted the ruling does not endorse the defunct Super League, which collapsed within three days of its 2021 launch after widespread protests.
The governing body said it would review the court's decision and could appeal to Spain's Supreme Court.
La Liga president Javier Tebas has criticised Real Madrid's legal challenge, arguing that it misrepresents the intent of the ruling.
Despite the backlash, Real Madrid remain one of the strongest advocates of the revived "Unify League" concept, keeping the battle for control of European football very much alive.
