The 31-year-old suffered a knock during the 2-1 win against Wigan last weekend and may not be risked for the game at the Hawthorns with a busy festive schedule to follow.
Hughton told reporters: "The good news is it is certainly not anywhere near as bad as either it could be or as we feared it might be - but I would have to say Grant is touch-and-go for the weekend.
"If he did miss West Brom, we would certainly hope he is fit enough for the rest of the Christmas period."
Hughton could turn to fit-again on-loan striker Harry Kane if Holt misses out as the Tottenham youngster has recovered from his long-term injury.
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Kane made a goalscoring return in his first action since September, notching twice for Norwich Under-21s against West Ham midweek.
The manager added: "Harry is certainly there or thereabouts. The decision we have to make on Harry is the fact he has been out for such a long time.
"Harry has done a fair bit of work, but he will be lacking in some areas, which is normal, but the good news is the injury is fine.
"It is good to have him back. If he was involved [at West Brom] it would be based on the fact he has done enough. We don't want him to break down."