Clattenburg has been accused by the European champions of making offensive comments, which are understood to have been interpreted as racist, during their acrimonious Barclays Premier League defeat to Manchester United on Sunday.
Chelsea lodged a formal complaint with the match delegate that saw the FA announce an investigation and Clattenburg stood down from officiating for a week. However the police then became involved after the Society of Black Lawyers demanded they look into whether a criminal offence had been committed.
The man behind the mooted black players' breakaway union, Peter Herbert, sent a letter to the Metropolitan Police Service (MPS), which read: "The Society of Black Lawyers wishes to record the incident that took place at Chelsea FC.
"Our information is that racist remarks were directed at John Mikel Obi and at Juan Mata. If so, that is wholly unacceptable in any circumstances.
"Although this matter may be investigated by the FA, it is appropriate that the MPS independently see if a racially-aggravated offence has occurred."
The police confirmed they had received the letter on Monday night but it is understood it was by no means certain an investigation would follow.
It is reported by the Daily Mail that Chelsea's players claim to have heard Clattenburg call Mata a "Spanish t**t", as well as abusing Mikel.
An FA statement read: "The FA has begun an investigation relating to allegations made following Sunday's fixture at Stamford Bridge between Chelsea and Manchester United (Sunday 28 October 2012).
"The FA will make no further comment at this time."
It has been confirmed that Clattenburg will not referee a Premier League game this weekend. The governing body said that "the intense level of scrutiny would detract from the match and be unfair to the clubs and fans."
Meanwhile, the referees' union has pledged its "full support" to Clattenburg. Prospect said in a statement: "Prospect is committed to helping to eradicate racism in football and in society generally. In the context of that commitment, Prospect is offering full support to Mark Clattenburg in relation to the allegations made against him."
The statement continued: "It is now important that the allegations are fully investigated through the proper process as quickly as possible.
"We will be making no further comment at this stage."
Mikel's agent and Chelsea refused to comment further on the matter but the club did confirm they had decided against holding a press conference to preview Wednesday night's Capital One Cup clash against United.
The Red Devils were similarly taciturn, although it is understood they were unaware whether any of their players heard Clattenburg's allegedly "inappropriate language" and could act as witnesses.
It is unclear how many Chelsea players witnessed what transpired but almost certain to be called upon should there be an investigation are Clattenburg's assistants and fourth official, with each connected by a microphone and earpiece throughout the game.
Former Premier League referee Graham Poll told BBC Radio Five Live: "If a comment of a racial nature was made, I think it should be reported and I think assistant referees will report it because there's no place for it."
Jeff Winter, who retired as a referee shortly before Clattenburg became a member of the top flight's Select Group, claimed the official's career was doomed if he was proven to have used racist language towards a player.
"If a match official has used racial insults or language to a player then he's for the high jump," Winter said. "He won't be getting a four-match or an eight-match ban, it'll probably be the end of his career, but that is if indeed he did say anything."
Leaders Chelsea's unbeaten start to the Premier League season came to an end when Javier Hernandez scored a dubious-looking 75th-minute winner for United after Clattenburg had shown red cards to Chelsea's Branislav Ivanovic and Fernando Torres in quick succession in the final half hour.
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