"nor be deprived of life, liberty, or property, without due process of law"
This portion of the 5th Amendment would apply.
Not even close. He's not being deprived of anything. He is free to work just not in the NFL.
Nothing in the Bill of Rights says that you have a right to work for whomever you want and make as much money as you want.
If it did we'd all be beer spokesman making millions working for Miller or Budweiser.