The highly-rated midfielder agreed a season-long loan switch from Tottenham Hotspur over the summer - on the same day that Tom Huddlestone swapped life at White Hart Lane for that at the KC Stadium.
Livermore has shone alongside Huddlestone in Hull's engine room, with the Tigers having made an impressive start to life back among the Premier League elite.
Bruce is now planning on discussing an extended stay for Livermore, with it hoped that competition for places at Spurs will play into his hands.
He acknowledges that the 23-year-old England international will not come cheap, but appreciates the need to take a few financial risks in order to consolidate a top-flight standing and give players of promise the stage their talent deserves.
Bruce said in the Sunday Mirror: "I would love to keep Jake if I could, so we'll have to see if there is a deal to be done.
"But I'm sure Daniel Levy, the Tottenham chairman, will want the Humber Bridge and the receipts that go with it for him.
"I haven't asked yet, but we shall do our utmost to see if we can make it permanent. At the moment, we are just happy to have him.
"The big thing for Jake is that he is playing games regularly. He has played eight games in a row in the Premier League for us this season, and that's something he has never done before. It is great for him, and he looks like he's enjoying it.
"When I eventually left Manchester United it was because I didn't want to be a bit-part player.
"We all want to play at the top but, when the big games come around and you are not involved, if you've got anything about you as a footballer you just want to get out and play somewhere."