Livermore has impressed during a season-long loan deal from Tottenham Hotspur, and Bruce is hopeful that a promising return to the Premier League will help the club in their attempts to secure the midfielder's services on a permanent basis.
"We've budgeted to be 20th, so anything on top of that might help me bag Jake Livermore, for example," Bruce told reporters.
"The first piece of business I'll try to do is to secure Jake if I can. I'll do everything I can to buy him. I think everyone knows my stance and, all things being equal, Jake would like to stay here.
"I would love to do something quickly, if we possibly can. Jake has indicated to us that he would like to stay, so we'll see how it develops."
Livermore has scored three goals in 37 appearances for Hull this season.