The Tigers boss is hoping to secure the services of the Red Devils winger either for the rest of the season or in a permanent deal
The 20-year-old Republic of Ireland international is in his second loan spell at the KC Stadium, having re-joined in November 2012 and Bruce has said that he is 'hopeful' of concluding a deal for the winger.
"We're still in discussions with Manchester United and hopeful we can get something done," Bruce told the Hull Daily Mail. "We're certainly doing our utmost to bring Robbie back here."
Brady has made 12 league appearances for the Tigers this season, scoring one goal and recently expressed his belief that the club could earn promotion to the Premier League.
Meanwhile, Hull are expected to formally conclude their transfer of David Meyler from Sunderland. The 23-year-old Ireland international underwent the final stage of his medical on Saturday, January 5.