Perhaps not. But if Hayward is valued enough by an organization, they'll make space to give him an offer. We do know there are a couple of coaches that probably value all he can do in Stevens and Hornacek and those organizations could clear enough space to make a max offer.
I think Lindsey was being honest in his interview. If you are Utah, the question you ask yourself is this:
Can you get a player in FA that is as good as, or better than Hayward? The answer is "no."
So, why in the world would you let Hayward walk for NOTHING if you are Utah. And, please, don't say "he is too expensive." Because, no matter the price, with the way Utah's salary cap situation is, he is NOT too expensive. So, if you are another team, the ONLY way you will get him is to give Utah the sun in return.
So, unless we get some unrealistic deal (which we won't, because Hayward isn't even an All-Star), Hayward will be back in Utah. And, unless you want to tie up your money for three days and get nothing in return, it is pointless to offer Hayward a deal (and piss off Lindsey).
So, all that being said, I don't think Hayward gets an offer from anyone else, and I think he comes back to Utah for a deal in the 11-12 per year range.