A video posted online showed Sterling being shouted at by a fan as he went to collect the ball from behind the goal.
No arrests were made but the Metropolitan Police issued a statement saying they would review footage to determine whether any racist abuse took place.
Chelsea, who won the match 2-0, said in a statement: "We are aware of a video circulating online in which it is claimed racial abuse was allegedly directed at a player at Stamford Bridge on Saturday.
"We will review the footage to determine whether any offences have been committed."
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Also on Saturday, two fans were arrested in Scotland for allegedly directing racial abuse at Motherwell substitute Christian Mbulu during his side's defeat at Hearts.
"The club abhors racism and all forms of abuse, and the individuals in question will receive indefinite bans from Tynecastle Park," a Hearts statement said.
(Reporting by Martyn Herman; Editing by Peter Rutherford)
