From the looks of it, Millsap is down to two suitors: The Jazz and the Thunder. It's like CJ Miles 2.0, except this time the winner gets a good basketball player. The other teams with cap money this summer are looking elsewhere for big men: Detroit (Villanueva), Portland (Turkoglu), and Memphis (Z. Bo). Atlanta is still a possibility, but with Al Horford cemented as their power forward, Millsap seems a poor fit in the Dirty South.
Oklahoma City on the other hand has money to burn. The team has a great salary structure right now. They have no bad salaries (worst is Collison's deal with two years left at 6.5). They have a bunch of talented youngsters who are still on their rookie deal. They are in a good spot. But, in a year or two they are going to have to pony up max money for Kevin Durant, and good money for Jeff Green and Russell Westbrook. Add those four to Millsap's expected deal (just south of 10 mil/yr) and you are probably paying around $60 million for 4 players. That's the same pickle that the Jazz are in.
The other tricky issue for the Thunder is where does Millsap fit on the team. Right now, the Thunder play Jeff Green at the four. Green is a slasher who is slightly undersized for a power forward. Are they thinking of playing Durant at the 2 and moving Green to the 3? Positionally I'm not sure that Milsap is the ideal fit.
But the Thunder couldn't give a damn about what I think. And the way their salaries are structured (cheap now, will be expensive later) is the exact opposite of the Jazz' structure (overloaded now, relief comes next year). If the Thunder offer Millsap a deal that is heavily front-loaded, the Jazz may blink. On the other hand, the Jazz can offer Millsap a deal that is cheaper up front and gets larger next year.
So, it all may depend on where Millsap would prefer to be. He can control his destiny, to a great degree. If he wants to be on the plains, he can sign a front-loaded deal that the Jazz probably can't stomach. If he wants to be in the mountains, he can just sign with the Jazz.