The Sun says England hitman Campbell notched 15 times in 34 games on loan to help City reach the top flight for the first time in their history four years ago.
Hull will have to offer £7.5 million to sign the striker.
Bruce admitted: "What I don't want to do is disrupt the team and the level of performance we are producing week-in, week-out.
"But what I keep asking myself is whether we score enough goals and do we need a natural finisher. That is what nags away at me."