Bridge of Sunderland (Photo: Reuters)
The 31-year-old former England international has only played once for manager Roberto Mancini this season in a 2-0 League Cup win over Birmingham on September 21.
Bridge joined City from Chelsea in a £12million move in January 2009, but has managed only 58 appearances in his three years with the club.
Bridge, who has 30 senior England caps, would fill a position which has been vacant for some time at the Stadium of Light.
He began his career with home-town club Southampton and hit the big time when he was snapped up by Chelsea in a £7million deal in July 2003.
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