London police launched their second football racism investigation this week on Thursday after a fan was pictured making a monkey gesture during Wednesday's League Cup match between Chelsea and Manchester United.
The Metropolitan Police received a complaint after the fan was pictured in British media, and said it is now investigating the "alleged racist behaviour at Stamford Bridge."
Chelsea is also investigating the incident during the 5-4 victory over United.
"The club will be examining all available footage and asks anyone who can identify the individual to contact the club," the Premier League leaders said in a statement. "Chelsea FC is committed to removing all forms of discrimination and if we have sufficient evidence we will take the strongest possible action, including supporting criminal prosecution."
Police are also investigating allegations referee Mark Clattenburg directed a racial insult at midfielder John Mikel during another meeting between Chelsea and Manchester United in the league on Sunday.
Chelsea has not complained to the police but sent a file to the FA on Wednesday as part of a formal complaint, citing Clattenburg's use of "inappropriate language" towards Mikel.
Chelsea has been involved in a series of race-related issues over the past year.
In March, the club banned for life a supporter who admitted racially abusing former player Didier Drogba.
The most high-profile incident concerned captain John Terry, who is currently serving a four-match ban after being found guilty of racially abusing QPR defender Anton Ferdinand by the Football Association.
Press Association Sport reported that Chelsea officials were planning to contact police themselves regarding this latest matter.
The club are also understood to be looking into a number of incidents concerning United fans after a pitch invasion and some objects were thrown onto the pitch during the match, which Chelsea won 5-4 after extra time.
Information from Press Association and The Associated Press was used in this report.