As reported by The Athletic, the Northern Ireland midfielder is understood to be in advanced talks with the Black Cats over a move to Wearside.
Evans was released by Blackburn Rovers at the end of last season, having played over 200 games across an eight-year spell at the club.
He was an integral part of the squad that won promotion from League One under Tony Mowbray, and continued to feature regularly in the second-tier thereafter.
With 66 international caps to his name, Evans is the brother of former Sunderland loanee Jonny Evans, who remains a popular figure after two successful spells at the club.
Evans’ arrival would bolster a midfield that has been short on experience since a number of significant summer departures.
Grant Leadbitter, Max Power and Josh Scowen all left the club at the end of their previous contracts, having played close to 150 games between them last season.