Hull have been forced to up their offer for Brady to £2million to match a bid from Watford, reports The Hull Daily Mail.
The 20-year-old is reportedly undergoing a medical with the Tigers.
"We're creeping along with Manchester United with regards to Robbie Brady," Bruce stated. "Robbie's loan deal was up so he went back and now we're in advanced discussions. Those went on late into the night on Friday and again over the weekend. We hope we can get it tied up. 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."