The Tigers boss says his club has opened talks with the R's regarding the 31-year old as they prepare for a promotion push back to the Premier League.
"We're talking to QPR. That's all we are at the moment, talking to them," Bruce told BBC Radio Humberside.
"We hope that we can try and resolve something next week if we possibly can and we'll see what develops."
He added: "I think the two chief executives are talking.
"Whether there's been a bid lodged just yet or not, I'm not quite sure where we're up to."
Campbell is out of favour at Loftus Road but recently enjoyed some good form in England's second tier when he scored 10 goals in 17 appearances on loan for Ipswich Town.