The 23-year-old was criticised for his decision not to wear a Remembrance Day poppy on his shirt during the Black Cats' 2-1 defeat at Everton last weekend.
The Republic of Ireland international subsequently received a mixed response from the travelling Sunderland supporters when he was introduced as a second-half substitute during Sunday's 3-1 victory at Fulham.
It is understood that threats have been directed towards McClean on Twitter, a social networking site which the player no longer uses, with police confirming yesterday they are investigating.
A statement released by Northumbria Police read: "Police are carrying out inquiries following a third party report of threats made on social networking sites.
"Officers have spoken to Sunderland AFC and inquiries are ongoing."
After yesterday's game, Black Cats manager Martin O'Neill confirmed McClean had received death threats, and backed him to rise above any negative reaction from fans concerning his choice not to wear a poppy.
O'Neill said: "James will deal with it (the booing).
"I think it is to do with the issue last week, it's a free choice in this world.
"James has lived with a lot of things - he's getting death threats too now so that doesn't help."