The 22-year-old winger spent the first half of the season on loan at The Valley, and the Addicks are keen to bring him back after coming under new ownership.
Championship rivals Leeds are also looking to tie up a deal, though, and are confident they can get their man.
Bruce admits a sale is likely to be sanctioned in the coming days, with Stewart left out of his side to face Middlesbrough in the FA Cup on Saturday.
The Tigers boss said in the Hull Daily Mail: "We were going to play Cameron but there's an interest from Leeds and they didn't want him cup-tied.
"I think we're close and we want to wish him the best of luck.
"He's had a particularly frustrating time but he's got himself back in good nick and he's another one who we'll try and help if we can."
Bruce also concedes that strike duo Aaron McLean and Nick Proschwitz could soon be on their way out of the KC Stadium.
He added: "Aaron's got to do the best for him. He's out of contract in the summer and we hope we can get him fixed up. Birmingham are still keen and a few others are.
"He never lets his chin go down but it's one of these things where he's not playing every week.
"Nick's in the same boat. There's been a few enquiries from Germany, which I expected, but we've got to find a solution.
"Like Aaron, he just wants to play every week on a Saturday for us. That's what they want to do but I can't guarantee that. Therein lies the problem."