Chelsea have identified and contacted a number of individuals in relation to the alleged abuse of Raheem Sterling.
Cameras appeared to capture a Chelsea supporter shouting what is alleged to be racist abuse at Sterling during Manchester City's 2-0 defeat at Stamford Bridge on Saturday.
A number of individuals were spoken to by Chelsea officials and Metropolitan Police officers at the end of the match. However, no arrests were made.
Chelsea, the Met and the Football Association are continuing to investigate the incident.
A Chelsea spokesman said: "We're aware of reports and video footage. We will investigate the matter and take the strongest possible action where necessary."
The Met Police said: "We are aware of a video circulating online in which it is claimed racial abuse was allegedly directed at a player at a Chelsea v Manchester City game at Stamford Bridge on Saturday, December 8.
"We will review the footage to determine whether any offences have been committed."
A Premier League spokesman added: "The club and the police are rightly investigating this serious matter.
"The Premier League and the clubs are opposed to all forms of discrimination in football and if anyone is found to have racially abused a Premier League player they deserve to be punished.
"We will support any action taken by the club or the authorities."