The Canaries are searching for a new manager after former boss Paul Lambert left to join top flight rivals Aston Villa.
Hughton, widely praised for his time in charge of Newcastle, had also been linked with the vacancy at West Bromwich Albion caused by Roy Hodgson becoming the new manager of England.
But the 53-year-old, who made his name as a player at Tottenham Hotspur, is now set for talks with Norwich, according to a BCFC statement.
"Birmingham City FC can confirm that Norwich City FC have made an approach for Chris Hughton with regards to their vacant managerial position," the statement said Wednesday.
"Hughton expressed a wish to speak to the Canaries and permission was reluctantly granted."
Acting Blues chairman Peter Pannu said: "Chris is a great manager and deserves the opportunity to speak to Norwich, which is why we have granted him permission to speak to them."
Lambert guided Norwich to back-to-back promotions from the third tier to the Premier League, with the Canaries finishing in an impressive 12th place.
Speculation linked Malky Mackay and Neil Lennon to the vacancy at Carrow Road, but the Canaries have confirmed their move for Hughton.
A club statement read: "Norwich City can confirm that Birmingham City have granted the club permission to speak to Chris Hughton about the vacant managerial position at Carrow Road.
"The club will be making no further comment at this stage."