PA Sport understands there is still a little way to go until any deal is clinched, but that the Black Cats hope to be able to unveil the 48-year-old sometime on Wednesday.
Sunderland have agreed to pay Bruce's current club Wigan a little less than ¦pound;3million in compensation and discussions have also taken place over the shape of Bruce's coaching team, with trusted allies Eric Black and Nigel Spink tipped to join him at the Stadium of Light.
That would have implications for the staff put together by his former Manchester United team-mate Roy Keane.
However, Ricky Sbragia has been promised a job for life at the club by Quinn after stepping in to plug the gap left by the Irishman when he resigned in December.
The chairman hinted in the wake of Sbragia's decision to stand down as manager after the final game of the season that the Scot's future role could be in the area of player recruitment.
That too will be one of Bruce's first concerns as he attempts to build a side capable of challenging for the Barclays Premier League's top 10 after a disappointing second campaign back in the top flight.
The Wearsiders survived by just two points and won only nine games despite investing almost ¦pound;80million in their squad in the two years since they won promotion.
New owner Ellis Shirt has promised to bankroll another recruitment drive, but is insisting on value for money.
The club has already been linked with moves for Tottenham striker Darren Bent and Wigan's Titus Bramble, Antonio Valencia and Paul Scharner.