Ricky Sbragia stepped down as Sunderland boss at the end of the season, having kept the team in the Premier League.
Former Celtic manager Gordon Strachan was linked with the vacancy before attention moved to Newcastle-born Bruce.
The former Manchester United defender began his managerial career at Sheffield United in 1998, and since then has had spells at Huddersfield, Crystal Palace, Birmingham and Wigan - twice.
His second spell at the Latics began in November 2007 after Whelan paid Birmingham £3m to secure his services, and this season he guided the Latics to 11th in the Premier League, while Sunderland finished 16th.
If Bruce does take the job, it will be the first significant change at the club since American businessman Ellis Short took total control of the club.
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