Hughton is believed to be the leading contender to replace new England manager Roy Hodgson at the Hawthorns. He was interviewed for the job 15 months ago before losing out to Hodgson.
But at that time Hughton was a free agent after being sacked by Newcastle two months earlier, and Birmingham are keen to retain his services.
A source close to City said: "Chris is very highly rated at Birmingham and has done a great job since taking over.
"Blues are planning for next season, want Chris to be part of those plans, and any approach would not be welcome."
Birmingham are anxious to avoid a repeat of last summer when manager Alex McLeish resigned and joined Aston Villa.