First, Peterson is just doing the math. He's got a lot of money headed his way, and he's not going to start taking fines. He can work this in the background more effectively and less costly.
Second, and the is my gut feeling, Peterson got word from his agent that the Cowboys, sight unseen, aren't going to pony up the type of offer that will pry him away from Minnesota at this time. Dallas is probably interested only in the 2nd or 3rd round pick range. The Vikings want a first rounder and more. Stalemate, for now anyway, and no other team is interested right now.
Peterson has to rebuild his value if he wants a team, primarily Dallas, to step forward and offer the kind of package that will get Minnesota's serious attention. The Vikings will gladly trade him for the right package, but they have to be able to sell this to their fan base. Otherwise, they'd just as soon have him on board to take pressure off of Bridgewater.
The Cowboys are really the only team in this mix, and right now, (1) they don't even know what they have in house, and (2) how that compares to what Peterson is now after his layoff. If they're going to pay Peterson the cash he wants and the Vikings they picks they want, they need to see him play some football. Best see that from afar for the time being.
No, this isn't dead if Dallas is truly interested. But it won't happen until preseason, or perhaps even the trade deadline. Both the Cowboys and the Vikings are more than content to just stand pat for now.
This negotiation will go down in to the 12th hour, many weeks from now.