Members of the Chelsea squad were reportedly subject to monkey chants upon arriving at their team hotel ahead of the fixture against Napoli in the last 16 of the Champions League.
Blues officials have warned their Italian counterparts that they will be reported to UEFA if similar incidents occur during the game on Tuesday evening.
A club spokesperson said: "Chelsea Football Club finds any form of discriminatory behaviour totally abhorrent and we believe it has no place in society whatsoever.
"If any members of our team or staff are subjected to racist abuse we would find that wholly unacceptable and it would be reflected in our conversations with UEFA."
Napoli had earlier issued a statement to home supporters urging them to behave, amid concerns that crowd trouble may lead to UEFA imposing sanctions on the club.