The 31-year-old forward has started just four games for relegation-threatened QPR since joining them in July 2011 and has spent much of this season on loan at Ipswich Town.
And Bruce has revealed the Tigers have identified Campbell as the man to bolster their attacking options.
"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."
Campbell, whose contract at QPR expires in the summer, has been a big threat in front of goal this term, scoring 10 goals in 17 Championship appearances for Ipswich.
Bruce and Campbell have a history together as it was the Hull City boss who signed the forward from Brentford during his time in charge of Birmingham City, before selling him to Leicester City for £1.6m in the summer of 2007.
"I think the two chief executives are talking," Bruce continued.
"Whether there's been a bid lodged just yet or not, I'm not quite sure where we're up to."
Bruce also added that Hull could sign a player from Egypt during the transfer window, but would not divulge any details.
"Certainly there's an interest in one in particular, but that's it," he explained. "It's not advanced at all, and we're still not too sure.
"The problem is work permits and there's all sorts of wrangles with that, but it's somebody I've been interested in for a little while, but that's all it is."