The alleged incident occurred when Lukaku celebrated scoring West Brom's third goal in a 4-2 win at the Stadium of Light on Saturday.
A spokeswoman for Northumbria Police said: "Police are carrying out inquiries after a report of racist abuse at the Sunderland v West Brom match on Saturday.
"The report was received at 10.10pm on Saturday, November 24."
Lukaku joined West Brom on loan from Chelsea in the summer and has scored four times in 11 Premier League appearances, only three of which were starts.
Sunderland said in a statement: “SAFC operates a policy of zero tolerance towards racism and anti-social behaviour of any kind and naturally we will co-operate with the police in fully investigating any such incidents.”