Bruce has identified Gibson as the man to replace Jordan Henderson, who will join Liverpool if they can compromise on a fee with Sunderland.
Gibson, 23, is on the fringes of United's squad but the Irishman has failed to command a regular first-team place and is one of a number of players who will be allowed to leave Old Trafford this summer if the right offer comes in. United value him at around ?6million.
Dis-United: Wes Brown and Darron Gibson are on their way out of Man United
Brown is another after falling behind Chris Smalling, Jonny Evans and the Da Silva twins in the pecking order to play in central defence or at right-back.
The 31-year-old former England defender has been at United since 1992, but his career has stalled and Bruce is ready to offer him a fresh start at the Stadium of Light.
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Explore more:People: Wes Brown, Steve Bruce Places: Liverpool, United Kingdom