Police are investigating "threats" made on social media against Everton players Jordan Pickford and Richarlison following Saturday's Merseyside derby.
Threatening tweets were sent to Pickford after he injured Liverpool defender Virgil van Dijk in a tackle.
Brazilian forward Richarlison was also sent racist abuse after he was sent off for a challenge on Liverpool midfielder Thiago Alcantara, the BBC understands.
Police said the culprits "are not beyond the law" and would face justice.
A Merseyside Police spokesman said: "The language used in the tweets is totally unacceptable and we are taking the reports extremely seriously.
"Those who use the internet to target others, and who commit criminal offences such as making threats or committing a hate crime in doing so, are not beyond the law.
"Detectives are making inquiries to identify the individuals who posted the tweets and where we identify offences we will take action to bring those responsible to justice."
Liverpool defender van Dijk suffered cruciate ligament damage when he was caught by the England goalkeeper Pickford in the first half.
The injury is likely to keep him out for at least six months and potentially the rest of the season.