"As far as I'm concerned Robbie Savage is and will remain a Birmingham City player," the Blues boss told the clubs official website.
"I can categorically deny that there has been any bid from Everton and I have gone so far as to speak to David Moyes and he has also confirmed this," added Bruce.
"Neither of us has any idea at all where this story appeared from and all people are doing is talking about something that is just unfounded speculation."