Perhaps the biggest thing in the way of the Jazz signing Millsap is their inability to offer him a max contract unless significant salary shredding moves are made. According to Basketball Insiders, even if the Jazz release all of their non-guaranteed contracts (including Millsap's brother Elijah), the Jazz would only have $16.6 million in cap space. Paul Millsap's max contract would start at somewhere around $18.6 million. If another team would be willing to offer Millsap a max deal, and there are indications that they would, Millsap would have to give the Jazz a discount in order to sign in Utah.
In other words, I think Millsap signing with the Jazz is pretty unlikely. I predicted in my column last week that Millsap would stay with the Hawks, Instead, I suspect the Jazz use their salary space more conservatively: on a wing player to play alongside Gordon Hayward, Alec Burks and Rodney Hood, or on a upgrade at the 3rd big position (just not one that's All-Star sized).