Bruce's new Blues vow
The native Geordie has been heavily linked with the Magpies, who have begun the process of seeking a replacement for the sacked Sir Bobby Robson.
However, Bruce told the Daily Star: "Let's make this absolutely clear, I have no intention of walking away.
"I owe that much to the supporters, the board of this club and to the players I have brought in and I have no reason to do that.
"I wouldn't resign. I have no reason to do anything like that to the people I work for."
Bruce signed a new five-year contract with the Blues in the summer and is just one of a host of names rumoured to be interesting Newcastle.
Middlesbrough's Steve McClaren, Aston Villa's David O'Leary and former England coach Terry Venables have also been linked with the St James' Park hotseat.