According to the Sun's Jamie Gordon, the three people in question claim the money used by Los Blancos for the purchase of the Welshman came from a bank previously rescued using public funds and thus was "indirectly state aid and a burden on tax payers."
"Spain was itself bailed out by European funds—making the issue a matter for Brussels," added Gordon.
Per Catalan outlet RAC1 (via Gordon), the accusations amount to a claim this could have led to Real having an unfair advantage over other clubs in their bid to sign Bale.
The report added that Bale, 26, is not implicated in any way to have acted inappropriately.
The winger moved from White Hart Lane to the Bernabeu late in the 2013 summer transfer window for a world-record fee of £86 million.
He signed a six-year deal and has won four trophies already in his fledgling Madrid career, including the UEFA Champions League and the Copa del Rey.
Earlier this year, details of Bale's contract emerged, which revealed Spurs have a first-refusal option on their former star up until June 2019 should any other Premier League side make a bid to sign him, per the Football Leaks website (via Marca's Juan Ignacio Garcia-Ochoa and Pablo Polo).
No doubt the north London side were attempting to legislate against him returning to England to join a direct rival, a smart move given his consistent links to Manchester United, per Rory Smith in the Times.
However, given his current form—13 goals and eight assists in 15 La Liga games this season, per WhoScored.com—it seems unlikely that Real would consider selling him to anyone just now.
Bale was not the only major arrival in La Liga in the summer of 2013. Neymar also made a high-profile switch from Santos to Barcelona in a transfer that continues to be investigated by the Spanish authorities.