It is understood the 24-year-old is close to agreeing a move to the Black Cats in the wake of the Blues' relegation from the Premier League at the end of last season.
Gardner, a lifelong City fan who began his career with derby rivals Aston Villa, has been in Bruce's sights for some time and the Black Cats registered their interest in him earlier this month.
He was part of the side which lifted the Carling Cup in February with a famous 2-1 victory over Arsenal.
However, he and his team-mates were unable to prevent Birmingham from slipping out of the top flight on a dramatic final day of the season, sparking speculation that his future, like those of several of his colleagues, could lie elsewhere.
Alex McLeish's departure as manager did little to alleviate the situation and it appears that one of new boss Chris Hughton's first duties will be to sanction his departure to the Stadium of Light.
Hughton admitted as he was unveiled earlier this week that he was expecting several of his high-profile players to go, and much as he had to when he took over at Newcastle, he may have to wait to discover which men he can retain before he can plot the way forward.
Bruce turned his attention to Gardner after selling England international Jordan Henderson to Liverpool in a move worth almost £20million, and with Bolo Zenden and Sulley Muntari having also left the club, he has a rebuilding job to do in midfield.
However, a successful swoop for Gardner would represent a signal of intent as he steps up his efforts to strengthen the squad which managed a 10th-placed finish last season.