Bruce has targeted the former Swansea striker after the collapse of Charlie Austin’s move from Burnley last week.
Graham, who failed to score in 13 games for Sunderland after a £5million move from South Wales last season, has returned from Paolo Di Canio’s training camp in Italy and he has been withdrawn from the Sunderland squad due to fly out to Hong Kong.
He is expected to meet Bruce in East Yorkshire.
Bruce is hoping to secure a year-long loan deal for Graham, 27, who was facing fresh competition for a place on Wearside following Jozy Altidore’s move from AZ Alkmaar.
Hull are hoping Bruce’s former club will agree to paying a portion of Graham’s wages to allow a loan deal to go through.
Although Alan Pardew was in the running for the player's signature in January, Bruce is expected to have a free run on the Gateshead-born forward.
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