Merseyside Police were unable to take action against the Instagram users who racially abused Liverpool's Trent Alexander-Arnold and Naby Keita after they were found to be based outside of the UK.
Monkey emojis were sent to both players on April 6 following Liverpool's Champions League defeat at Real Madrid.
The abusive comments were removed by Instagram and reported to the police.
Merseyside Police told Sky Sports News they have closed their investigation because all the offending users were traced outside of the UK.
A spokesman for the force said: "Following a full investigation, all the offenders were identified from their social media accounts but all were based abroad so no further action was therefore taken."
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