Merseyside Police said it had received reports that six Liverpool fans in total were attacked in the Italian city.
Local police in Naples said the victims included a British family of four.
The Merseyside force, which has officers in the city liaising with local police, said two fans, men aged 27 and 53, were taken to hospital with stab wounds. Their injuries are not thought to be life threatening.
Naples police said three local men had been arrested.
"We are still gathering information," a Naples police spokesman said.
"Four people of the same family, a father, a mother and their two sons, were attacked last night and needed medical attention.
"Due to the aggression, three Naples citizens were arrested."
Local police are planning to hold a press conference later at which they are expected to release more information.
Liverpool are due to play Naples later.