The defender has been told he can leave the club this summer.
Paolo Di Canio attacked his ‘arrogant and ignorant’ Sunderland players after saying he was disgusted by images of Bardsley plastered in the money after a night out.
The Sunderland manager dropped Bardsley and fellow reveller Matthew Kilgallon for last season's game at Tottenham and had earlier revealed he had fined five other players late last season alone.
Di Canio insisted none of the fined players will play for him again and vowed to stamp out a drinking culture at his club.
The Sunderland boss said last season: ‘That is something really wrong. It’s disgusting me even to see the image for the club.
‘It’s not about going out with your friend and getting back at two o’clock or three o’clock, which is late. You can close one eye. But not full of alcohol and walking like this. They have to behave well.
‘There is no excuse to behave like he (Bardsley) did. From now I will be more strict because we have to improve our professionalism.'