The Baggies are poised to ask Blues for permission to speak to Hughton in the next 24 to 48 hours.
Albion have held talks with former Chelsea manager Claudio Ranieri and ex-Manchester United and Chelsea midfielder Ray Wilkins as they seek a replacement for new England boss Roy Hodgson.
But it is understood Hughton remains the preferred option of Baggies chairman Jeremy Peace.
Hughton has remained the overwhelming favourite with bookmakers despite Albion interviewing other candidates.
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 Premier League last season.
Hughton came close to taking over at the Hawthorns 15 months ago when a free agent after leaving Newcastle, before being pipped to the role by Hodgson.
Hughton replaced Alex McLeish at St Andrew's last summer and steered Birmingham to the npower Championship play-offs despite the majority of the squad from their last season in the Premier League departing the club.
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