The Ivorian international defender joined the team when they were in the Premier League in 2016, but since then they have dramatically fallen down in to the third tier of English football after two successive relegations.
The former Lorient player made 24 appearances for the team last season as they struggled in the Championship, and is now close to joining Strasbourg in Ligue 1 on loan, with an option to buy, according to 'Sky Sports'.
While Kone is leaving Wearside, Bradford's Charlie Wyke is joining the club from fellow League One outfit Bradford City.
The forward came up through the youth system at Sunderland's rivals Middlesborough, before moving to Yorkshire in 2017.
He has experience of the league which Sunderland will look to get out from at the first attempt, after scoring 19 goals in 37 appearances in League One in the past two season for the 'Bantams'.
'Sky Sports' report that he will have a medical at the Stadium of Light, before being unveiled as the 11th signing of the summer window by the 'Black Cats', as they look to rebuild their reputation after such incredibly bitter disappointments in the last few years.