His daughter Abby seems to think he should. According to New York Magazine, Abby tweeted out last night "Trying to convince dad @JonHuntsman to run for mayor of NYC. Thoughts? #whynot?"
The magazine says it kinda makes sense.
It's certainly true that Huntsman's moderate (dare we say Bloombergian?) Republicanism and urbane sensibility would play far better in a place like New York than nationally. But while Abby Huntsman lives in New York, neither of her father's two houses is here, and he'd have to make New Yorkers forget about that. But just as with now-unlikely mayoral candidate Ray Kelly, there's probably no harm and a certain amount of benefit for Huntsman in having his name linked no matter how loosely, by a relative who perhaps misses the spotlight, to the race.