Livermore has enjoyed an impressive first half to the season with the Tigers, and after rejecting suggestions that the 24-year-old had returned to White Hart Lane, Bruce admitted that he would like to strike a permanent deal in the summer.
"Jake's had a wonderful five months here. He's benefited his career by playing. We've given him that platform and he's certainly grabbed it," BT Sport quotes the 53-year-old as saying.
"The last thing that we wanted to do was to lose him in January because we'd like to do something permanently if we possibly can.
"We knew that it wasn't going to be possible this month but it's still the case that we'd like to bring him to the club, that hasn't changed."
Livermore has scored twice in 23 appearances for Hull this season.