The Black Cats have advised McClean to shut down his account after the Northern Ireland-born Republic of Ireland international posted that his favourite song was The Broad Black Brimmer Boy by the Wolfe Tones.
The song lyrics tell the story of a boy whose father is killed fighting for the IRA with McClean's post offending the Democratic Unionist Party (DUP).
"On flight for the maras game. Only one thing for it - headphones in, Wolfe Tones on! What's everyone's fave song? Broad Black Brimmer edges mine," he posted.
DUP MP Gregory Campbell was quick to lambast McClean and urged him to stick to football.
"As someone playing football at a professional level for Sunderland, McClean should be an example to young people. It is obviously up to his manager... to decide what course of action to take now," he said.
"Three simple words should suffice - stick to football. If he doesn't heed this then a final three words should be given - pack your bags."