Former Toon head coach Bruce tried to bolster the playing squad but the only arrival was Joe Willock from Arsenal for £20million.
Pederson, who has been at Birmingham since 2018, was contacted by the 60-year-old but revealed the interest did not progress.
He told Danish publication Bold: “It was close with Newcastle in the summer. The club (Birmingham) got a call from Steve Bruce.
"He said he really wanted me, but it didn’t work out in the end, because there were some things that had to succeed before the ends could meet.
“Of course, it’s too bad it didn’t happen, but there’s nothing to be done about it.
"It would have been a really good opportunity for me, but yes, it did not happen, and now they have got new owners and have got other muscles to play with, so I do not know exactly how it is anymore.”
Pederson has now enter talks over a new contract at St Andrew’s.
He added: “We’re in dialogue, and they’d like to extend. I’m happy to be here and focus on doing well for the club, but now we’ll see what happens.
"I have set a goal from the start that I want to be in the Premier League.
"I have played a few years in the Championship, where I have been and still am really happy at Birmingham, so I feel ready and that is my biggest dream."