Premier League referee Mark Halsey has made a complaint to Greater Manchester Police after receiving two abusive tweets.
And the 51-year-old has asked the police to investigate the matter, Professional Game Match Officials Limited (PGMOL), a spokesman confirmed.
The abusive tweets come just days after the UK's director of public prosecutions Keir Starmer said new guidelines for prosecutors on social media cases will be issued in the wake of a number of growing complaints.
Last week, a Welsh Premier League footballer who posted an abusive message about Olympic diver Tom Daley was not charged because the message was "not so grossly offensive that criminal charges need to be brought", he said.
But Mr Starmer, the most senior prosecutor in England and Wales, added: "The time has come for an informed debate about the boundaries of free speech in an age of social media."
Halsey made two controversial decisions on Sunday, both of which went in favour of Manchester United, sending off Liverpool midfielder Jonjo Shelvey before awarding United a penalty, which was scored by Robin van Persie.
Two tweets were sent out by disgruntled Liverpool supporters following the game, both of which were met with outrage from other Twitter users.
One post, from an account named @johnwareing1, read: "I hope Mark Halsey gets cancer again and dies", while another from @lfcjohn259 read: "Mark Halsey should've died of cancer."
The post from @lfcjohn259 was deleted and the @johnwareing1 account was removed completely.