The Norfolk club, who finished 12th in the Barclays Premier League last season, are without a manager after Paul Lambert left to join Aston Villa.
Norwich see Hughton as the man to take the reins from Lambert and continue their remarkable rise up the football ladder.
Hughton guided Birmingham to fourth in the npower Championship last term but his team were knocked out of the play-offs by Blackpool, who went on to lose to West Ham in the final.