Burrows is in his second season with Blues but has failed to settle and for most of his time at the club he has been left on the sidelines.
Last season Burrow's had a similar fall-out with ex-boss Trevor Francis when he wasn't picked for the Blues' Worthington Cup final squad.
Steve Bruce has no intentions of making this current fall-out public and has denied that the defender has been fined or transfer listed.
He told the club's official website: "It's an internal matter and I don't want to give any public statements.
"He's been disciplined and we'll keep it internal.
"I've never suspended or fined him and I've told him to come back when he wants to train properly."