Chelsea and the Metropolitan Police have launched an investigation after an incident of alleged racist abuse was highlighted on social media on Saturday.
Twitter users highlighted a first-half incident when a fan appeared to abuse Manchester City forward Raheem Sterling.
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.”
No arrests have been made, the Met added.
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The Blues won the match 2-0 thanks to goals from N’Golo Kante and David Luiz.
City tasted defeat for the first time in the Premier League this season, meaning Liverpool are still top of the division.