My guess is we have a slightly less than 50% chance of getting him. I think he had problems with Utah early in his career, but they've done a good enough job of surrounding him with talent, only they don't have another clear offensive star or ways to get one.
Reasons to stay:
1) His family is probably comfortable in Utah.
2) He demonstrated loyalty to Stevens when he was a teenager, it would be difficult for him to leave a franchise that has for the most part done him right and has a good coach now in Snyder.
3) They have Gobert manning the middle, the Celtics have no one like that and no obvious way of getting one. Chances are they won't get anybody close to his level in rim protection anytime soon. Put it this way: It would be easier for Utah to find a guard who can score 25ppg than it would be for the Celtics to find a big man who is an annual defensive player of the year candidate.
Reasons to leave:
1) Jackie Mac said on the Ryan podcast that when she asked him how often he actually talks to Stevens, he said not often. So she thinks the Stevens connection is overstated. That being said, if he WERE to leave Stevens being here would definitely be a positive as opposed to an unknown.
2) The money thing is not a huge deal. The extra year doesn't matter as much as people think and there's always the option to sign for less years and go on the market again in his early 30s and get another mega deal.
3) Boston has the resources to improve their team, Utah doesn't (though both will be capped out soon)
4) He wouldn't have to be the sole face of the franchise and chief offensive threat. Some players don't want that responsibility.
5) If he views GS as being more dominant in the West than Cleveland will be in the East in the next few years (LeBron is older than the "core four" of Durant/Curry/Green/Thompson).
6) Boston is a bigger market and gets more attention. Even if he's not Mr. Publicity, some players would rather play on a bigger stage. I think Horford did like the idea of playing for Boston for this reason vs. Atlanta which has always had an apathetic fan base.
7) Stevens' system will allow Hayward to elevate his game and is more enjoyable to play.
Ainge and this ownership group have proven they know not just how to win a title but are willing to pay for it. It's not clear Utah will ever be one of those ownerships willing to go high over the cap or pay the luxury tax.
So even though I thought of a lot more reasons for him to leave, I think it would still be very difficult decision for him to make due to the family thing and Gobert. If he craves a little more excitement and the big stage and slightly better title odds, I think Boston gets the nod.
Edit: I want to add that he's best buds with Joe Ingles though it would be hard for Utah to keep both Hayward and Ingles anyway. Also, that apparently Utah has gone into luxury tax territory before, so I was wrong about that.