The incident happened in the first half at Stamford Bridge as Sterling went to retrieve the ball.
The Metropolitan Police says it is “aware of a video circulating online in which it is claimed racial abuse was allegedly directed at a player.”
In a statement, the force says “we will review the footage to determine whether any offences have been committed.”
Chelsea has been at the forefront of anti-racism campaigns.
The club says “we will investigate the matter and take the strongest possible action where necessary.”
Chelsea won 2-0.
Source: Fox Sports