The 52-year-old is targeted after handing out red cards to West Ham and Southampton players in recent games.
Police are investigating death threats and abusive messages sent to Premier League referee Mike Dean and his family.
The messages began after the 52-year-old made the controversial decision to send off West Ham midfielder Tomas Soucek in Saturday’s game against Fulham. The red card was overturned on appeal.
Four days prior, Dean sent off Southampton’s Jan Bednarek at Manchester United – a decision which was also overturned.
As a result of the abuse, Dean has asked not to be involved in a Premier League match at the weekend.
He has reported the messages to police, and a Merseyside Police spokesperson confirmed enquires were ongoing.
“Threats and abuse of this nature are totally unacceptable and we fully support Mike’s decision to report these messages his family received to the police,” said Mike Riley, a former Premier League referee who is general manager of England’s refereeing body.
“Nobody should be victim of abhorrent messages like this. Online abuse is unacceptable in any walk of life and more needs to be done to tackle the problem.”
Dean will be in charge of the FA Cup fifth-round tie between Leicester and Brighton on Wednesday night, but asked not to be involved in a Premier League match at the weekend.
For both Bednarek and Soucek, Mr Dean consulted VAR and checked the incidents on the pitchside monitors.
Bednarek was sent off for a challenge on Anthony Martial in Southampton’s 9-0 loss to Manchester United but an appeal to the FA by Southampton led to that decision being rescinded.
Soucek was sent off in stoppage time during West Ham’s 0-0 draw with Fulham for catching Aleksandar Mitrovic with his elbow.
West Ham manager David Moyes said after the game he was “quite embarrassed for Mike that he would have made that decision” and the FA decided ultimately that the club’s appeal was legitimate.
“I am disappointed with football in general that the officials would allow these situations to take over from the game,” Moyes said on Monday.
“I can only see the officials being the people that can stop it by not allowing the players to get away with the actions they are taking, because it is making the referee’s decision so difficult in giving them a decision when there wasn’t one to give.”