The investigation is taking place amid an increasingly bitter battle for the leadership of the 1.4 million member Unite union.
Mr McCluskey, who has repeatedly aligned himself with left-wing Labour leader Jeremy Corbyn, claimed in an interview with the Observer on Sunday that he is the victim of a right-wing plot to undermine him.
Sources close to Mr Coyne have become increasingly confident he will topple the current leader when the result is announced on April 28 — with an unusually high turn-out for a union election showing enthusiasm for his more moderate message.
Mr McCluskey said as a Labour member for more than 45 years he had never experienced any form of antisemitism.
His comments were in stark contrast with Mr Coyne, who told the audience on the BBC’s Question Time on Thursday last week he had become a victim of “hate crime” after his JC interview.
Following the article an individual using the Twitter handle @1UnionBloke, sent Mr Coyne a slew of offensive messages. One showed a picture of Mr Coyne next to a man with the Star of David on his body and brandishing a gun. The caption read: “Be warned @gerard_coyne has backing now!! Jewish Mafia.”
Other messages from the account included suggestions Mr Coyne was pandering to the Jewish community in his leadership campaign.
One tweet said: “His anti anybody who isn’t Jewish is exposed. @gerard_coyne also reveals his shadowy backers. So @UniteforLen.”
A photograph of Mr Coyne’s house was also posted on Twitter.
The JC has approached West Mercia police for comment.
