Bardsley was already out of favour on Wearside when pictures emerged of him at a casino just days before Sunderland's final game of last season.
He was not included in the club's Premier League squad list when it was announced last week, and a comment on Saturday night, purportedly from the player himself, read: 'Great opening day. Hahahhahaha!!!'.
It is understood the full-back has now been told to stay away from the club's training ground while the incident is investigated.
Sunderland's longest-serving player - who is in the final year of his contract - was expected to leave over the summer but broke his foot playing for the reserves last week, making an exit during this transfer window unlikely.