The Daily Mail says Birmingham are unlikely to make life easy for West Brom and have the option of refusing them permission to speak to Hughton, who is operating on a one-year rolling contract.
But their hand is likely to be weakened by the uncertain financial situation at the club.
Birmingham are currently operating under a transfer embargo after failing to produce their annual accounts. The club's owner, Carson Yeung, is also awaiting trial in Hong Kong on money laundering charges.
In contrast, Albion run a sound financial ship and Hughton would inherit a squad which finished 10th in the Barclays Premier League last season.