Bruce, who has 20 months to run on his existing deal, admitted after Sunday's 2-1 defeat at Blackburn that his six-year reign may be heading for a savage end.
But Bredbury, a manager with first-hand experience of Yeung's alleged interference, fears Manchester United legend Bruce will only be on borrowed time if he remains.
Now coaching at Hong Kong First Division side Tai-Po FC, Bredbury suspects Bruce's face may not fit into Yeung's plans to transform Birmingham into a global brand.
He told the Mirror: "Carson Yeung will want to do things his way and make an impact. Whether that means getting rid of Steve Bruce or making some substantial investments, he will want to put a marker down.
"Maybe he is looking at Bruce and thinking his face does not fit. He wants this club to be a recognised brand across the world and Bruce might not be a big enough name for him.
"I would be concerned if I was at Birmingham - there must be serious doubts about who is behind him and how he is going to run things."