Valencia have reported death threats made to president Anil Murthy to the police.
Murthy, members of his family and employees at the LaLiga club have also been targeted by fans.
Valencia revealed back in October 2019 that the club had informed police of death threats made to Murthy.
With Jose Bordalas' side 11th in LaLiga and losing to Real Betis on penalties in the Copa del Rey final, supporters are alleged to have crossed the line again.
A club statement said: "Valencia CF, through the club's legal services, are compiling all death threats, insults and other actions against president Anil Murthy, his relatives and club employees.
"This Wednesday morning, these actions have been reported to the police, and in the coming days an update of the complaint will be carried out, including reporting demonstrations of hatred and threats of acts of violence carried out on social networks.
"This type of behaviour is not acceptable in society, it does not represent any of the values of Valencia CF and may lead to legal consequences."
The club earlier this month called on their supporters to respect Bordalas as they condemned "the harassment" of the coach and his players.
Bordalas was appointed as Valencia before the start of the 2021-22 campaign, just two days after departing Getafe following a successful five-season spell.
The 58-year-old was chosen by Valencia owner Peter Lim as the successor to Javi Gracia, who became the 11th coach to leave the club in the past nine years.