Robins owner Steve Lansdown is believed to have placed a price tag of £10m on Flint, and Birmingham are thought to have fallen well short of that valuation with their initial offer.
"We put in [a new] offer," Redknapp told the Birmingham Mail today. "I don't know where it's at to be honest with you. There is an offer gone in.
"It depends what his price tag is. They've got four centre-halves or five so he's a good player not to play.
"We'll only make an offer of what we think he's worth. If it doesn't meet their valuation there's nothing we can do about it but we'll move on."
Redknapp also confirmed that the club had not submitted a fresh offer for Bryan.