The Trotters have put Archie Knox in charge of first-team affairs following the departure of Sammy Lee by mutual consent on Wednesday.
Wanderers have approached the Blues to ask permission to hold talks with Bruce but the City board has refused permission.
A City statement said: “Birmingham City FC can confirm they have received an approach from Bolton Wanderers seeking permission to speak to manager Steve Bruce in relation to the vacant manager’s position at Bolton Wanderers Football Club.
“The club has refused to give Bolton permission to talk to Steve Bruce as he is currently under contract with Birmingham City. We now consider the matter closed and will not make any further comment.”
Bruce has been at St Andrews for six years and twice steered the club to promotion to the Barclays Premier League. But he has become unsettled after prospective new owner Carson Yeung refused to rubber stamp the new contract he agreed with the current board of directors.
Bruce has 20 months to run of his current deal and in the past has stated his desire to remain with Birmingham long-term.
However, he could be tempted by a move to the Reebok Stadium as a successor to one of his closest friends in football, Sam Allardyce, who has moved on to Newcastle.
In the meantime, Knox takes charge at the Reebok. Knox was appointed by Lee as coaching co-ordinator in August and will look after the team as they prepare for the hugely difficult trip to the Emirates Stadium to face Arsenal tomorrow.
It is thought the 60-year-old, who left his post as Scotland Under-21 coach, will be assisted by first-team coaches Jimmy Phillips and Ricky Sbragia.