Liverpool chief executive Peter Moore has called on fans in Barcelona to "act in a manner befitting LFC" after minor disturbances in the city on Tuesday.
Videos have circulated on social media apparently showing individual supporters, in different incidents, pushing locals into a fountain at Placa Reial, just off La Rambla.
Later in the evening police cordoned off the square and forced all fans back on to the main tourist strip before walking them up the street to Placa de Catalunya, a main transport hub, where they dispersed.
Merseyside Police say they are aware of the video:
On Tuesday, as thousands of fans began to arrive in the city for the Champions League semi-final first leg, Merseyside Police's dedicated Twitter account for LFC fans tweeted the advice: "Eat, drink and enjoy all areas in the city centre. Respect monuments."
Liverpool, as a club, condemned the behaviour as "totally unacceptable".
Meanwhile Merseyside Police confirmed six men were arrested by Spanish Police on Tuesday night on suspicion of public order offences following an unrelated incident.