The Wearside club are on the lookout for a replacement for Belgium international Simon Mignolet, who last week completed his move to Liverpool, and manger Paolo Di Canio has targeted the 25 year old to fill the void.
Mannone has been with the Gunners for eight years, but has made just fifteen Premier League appearances having been behind Jens Lehaman, Manuel Almunia and Lukasz Fabianski during his time at the Emirates.
Wojciech Szczesny is their current first choice, while there are strong reports linking the club with a move for a new number one themselves.
Mannone has also had loan spells with Barnsley and Hull City, joining up with the latter twice in the last three seasons.
Talks between the Sunderland and Arsenal are at an advanced stage, with the player expected to discuss personal terms next week ahead of the proposed move.