The 28-year-old has been pushed out of the Black Cats squad following manager Paolo Di Canio's rage at the player last season after he was pictured at a casino.
According to the Sunderland Echo, Black Cats Under-21 player Scott Harrison posted a photo of the tunnel at the Stadium of Light with the caption "#opening day" ahead of the 1-0 defeat.
Following the match, Bardsley is said to have commented on the photo with the message: "Great opening day. Hahahhahaha hahahhaha!!!"
Bardsley has not been given a squad number by Di Canio.