The striker previously enjoyed a successful loan spell at the KC Stadium in 2007 while he was owned by Manchester United.
Reports had suggested that Bruce, who worked with the 24-year-old as the Black Cats boss, had held discussions with his former club about a possible loan move for Campbell.
"As far as I am aware, Fraizer is not available to loan at present," said Bruce.
"If he was available, of course we would ask the question, but at this time, that's not the case."
Campbell scored 15 goals in 34 appearances during his loan spell at the Tigers.