Gyan, 25, has been heavily linked with Spurs - who are looking for a new forward after Jermain Defoe, Peter Crouch and Roman Pavlyuchenko failed to fire last season - as well as Real Madrid and Udinese.
However, Bruce says he has no interest in selling Gyan, who has scored 11 goals in 33 appearances for Sunderland following a £13 million move from Rennes.
"I haven't had a telephone conversation with any agent, no offer from any club," Bruce told BBC Newcastle. "He's going nowhere unless we get a wonder bid that comes out of nowhere.
"As far as I'm concerned, I'm looking forward to seeing Gyan being ready for the Premier League better than what he was last year. I think he'll be better - he knows what to expect and I'm expecting big things from him."
Despite bringing in two strikers already this summer - Connor Wickham and Ji Dong-Won - Bruce has confirmed that Gyan will remain a first choice for the Black Cats.
"In the Korean boy and Connor Wickham they're both physically big, they will lead the line," he said. "They're young, and haven't played at this level before which is always a risk, but for the future of the club I'm convinced that they're two very good young players."
Sunderland also told Sky Sports News that there is no truth in reports they are lining up bids for Tottenham striker Defoe and Wigan winger Charles N'Zogbia.