Scotland Yard said an investigation was launched into alleged comments during the match at Stamford Bridge on October 28.
Police said in a statement: "Inquiries were made and no victims have come forward. The matter will remain as a recorded incident. Without a victim and/or any evidence that any offence has been committed, the matter cannot currently be investigated."
The statement continued: "If the situation changes and a victim and/or evidence to support an allegation of a crime comes to police attention, then further inquiries will, if appropriate, be made."
The 37-year-old referee returned to training with the top-flight Select Group of referees last weekend for the first time since Chelsea's complaint.
Chelsea have alleged that Clattenburg used a term understood to have been interpreted as racist towards midfielder John Obi Mikel.
The official strenuously denies having done so.
Clattenburg and referees chief Mike Riley decided jointly that he should not be in charge of matches while the case has been going on.
The FA is yet to make a decision on the matter after conducting its own investigation.