The 20-year-old winger had been on a short-term loan deal with the Championship club and it is understood that United have now accepted an offer from Hull City, believed to be in the region of £2 million.
Hull boss Steve Bruce told the Hull Daily Mail: "We're creeping along with Manchester United with regards to Robbie Brady.
“Robbie's loan deal was up so he went back and now we're in advanced discussions."
He continued: "We hope we can get it tied up and fair play to the board again because they're doing their utmost to make it happen. For that I'm entirely grateful.
"I would hope for a bit of good news, possibly at the beginning of the week. That would be a huge addition because of how well he's done.”
Brady arrived on loan at the KC Stadium in November and has scored one goal in 12 games for the Tigers.