Officers are probing the messages, which were sent after it was reported that the Liverpool forward is moving to Manchester City for £49million.
Many of the tweets have since been deleted but some Twitter users took screen grabs of the threatening messages and urged Merseyside Police to investigate.
A spokesman for the force said: “We are taking the incident extremely seriously and an investigation by detectives in Liverpool CID is on-going.
“People who use the internet to target others and who commit criminal offences such as harassment or hate crime are not beyond the law and can expect to be brought to justice.”
Sterling is expected to have his medical at City on Tuesday.