Police fired tear gas to calm Liverpool fans, according to the Daily Star.
It is also noted that one of the fans turned to BT Sport with a message that children were also injured due to police actions.
According to a scoreboard at the Stade de France in Paris, the start of the game was delayed due to the late arrival of fans.
However, later it became known that some fans were able to enter the stadium bypassing security and law enforcement agencies had to close the passages.
Liverpool have seven victories in the main club competition in Europe, while Real Madrid has 13.
Earlier it was reported that Liverpool and Real Madrid started the pre-match warm-up before the Champions League final half an hour late.