The 23-year-old midfielder, who joined the Tigers on a season-long loan deal from Tottenham Hotspur last month, played an important part in their 3-2 away win against Newcastle United on Saturday.
"We are delighted the pair (Livermore and Tom Huddlestone) of them have come and joined us," talkSPORT quotes Bruce as saying.
"I hope we can afford Jake if he ever becomes available from Spurs and Tom's a really wonderful footballer. There are people here who enjoy playing with him."
Hull are currently 10th in the Premier League table with seven points from five matches.