Chelsea and the Metropolitan Police have opened investigations after a spate of alleged racist abuse was reported on social media on Saturday.
Twitter users pointed to an incident in the first half when a fan apparently abused Manchester City striker Raheem Sterling.
A Chelsea spokesperson said, "We know reports and video footage. We will investigate the matter and, if necessary, take the strongest measures. "
"We will check the footage to see if any violations have been committed."
There were no arrests, added the Met.
The Blues won the game 2-0 thanks to goals from N & # 39; Golo Kante and David Luiz.
The city was defeated for the first time this season in the Premier League, Liverpool thus remains at the top of the division.