Bale has been strongly linked with a free transfer to his hometown team following the end of his turbulent nine-year spell in Madrid.
Following the game on May 28, Gerald Darmanin claimed that between 30,000 and 40,000 Liverpool supporters either came to Paris without tickets or with fake tickets.
The club's call for answers came six days after problems occurred outside the Stade de France in suburban Paris, where Madrid won the European title by defeating Liverpool 1-0.
Darmanin threw his full support behind the police and security officers who were in charge of policing the event.
Bale was booed the few times he got to play this season and was even jeered by some during the team’s title celebrations after it won the Champions League a record-extending 14th-time last week.
"There's no doubt, it's very clear that Benzema had a spectacular year," Messi said in an interview to Argentine TV channel TyC Sports when asked if Benzema should get the prestigious award.
A week earlier, the club was mired in disappointment and trying to understand why it was turned down by the young French star who had always said he dreamed about playing for Real Madrid.
The French government has faced a barrage of criticism from press and politicians in Britain over police handling of the match on Saturday, which saw thousands of Liverpool fans struggling to enter.
The veteran left-back revealed his plans after the team's 1-0 Champions League triumph over Liverpool on Saturday.
The final was delayed for 37 minutes and kicked off as security was still struggling with the flow of frustrated supporters into the Stade de France.
It was another blow for Mohamed Salah who was reduced to tears twice earlier this year following Egypt's losses to Senegal in both the African Cup of Nations final and the World Cup play-off.
Pre-match crowd problems overshadowed this final, and are sure to be the focus of an investigation by UEFA and authorities in the coming days.
Thousands of soccer fans were descending on Paris to see Liverpool and Real Madrid meet in the Champions League final later Saturday.
Speculation has mounted over the future of the 30-year-old, who has been linked with Barcelona and Bayern Munich as he prepares to enter the final year of his contract at Anfield.
Real Madrid stands in the Reds' way at the Stade de France on Saturday, just as they did four years ago in the first of Liverpool's European Cup finals under their German guru.