Brady is expected to agree to a permanent switch to the KC Stadium in the next few days after a successful loan spell and despite counter offers from Sunderland and Watford.
"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," said Steve Bruce.
The Hull boss has already sealed a deal for David Meyler and a successful pursuit of Brady would bring his spending on Irish talent to £3.5m.