Bruce, who recently signed a new five year contract with Blues, has been installed as the bookies second favourite behind former Liverpool boss Gerard Houllier to take over the managers job with the club he supported has a boy.
"Steve is manager of Birmingham City and I do not feel that is going to change for the foreseeable future," the Blues chairman has said.
"He's ambitious but he's a young man. He can bide his time and finish his job at Birmingham City.
"A few years ago leaving Birmingham for Newcastle would have been understandable because the gap between the clubs was so huge.
"That gap has shortened under Steve Bruce and you could argue that Newcastle is currently a club in turmoil."
Bookies make Houllier the 7/4 favourite to take over from Sir Bobby Robson with Bruce priced at 5/2 and Alan Shearer 11/4.