O'Neill, whose last managerial job was at Villa Park, has been regularly tipped for vacant posts at high-profile teams in the last 12 months and was the bookmakers' favourite.
The Black Cats are 16th, two points above the relegation zone, which led to Bruce's sacking on Wednesday.
The team has won only two of their 13 league games this season.
O'Neill, a former Nottingham Forest player, built his managerial reputation at Wycombe Wanderers before successful spells at Leicester City and Celtic.
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