The 37-year-old official has been accused of using "inappropriate language" in two incidents allegedly involving John Obi Mikel and Juan Mata during Chelsea's controversial 3-2 defeat to Manchester United.
Now, the Society of Black Lawyers have asked the police to begin a criminal investigation to determine if the language used was racially offensive.
A statement from the organisation 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."
Clattenburg's career highlights include officiating the 2012 League Cup final and the men's Olympic gold-medal match at London 2012.