If it is to happen, the most likely scenario is that Dallas keeps him this year while aiming for a SB; then next year trade while on his fifth year option. They have the money to sign him, truly, but that means you are spending north of $110M on three players (presume 35M on Lamb, 35M on Parsons new deal, 40M on Dak) and filling out the rest of the roster with guys making no more than $10M on the FA market and draft picks, or cutting guys that help them stay competitive like Steele or Diggs.
The likelihood of him ending up in Chicago is incredibly low - I would bet that Poles prefers to not spend the kind of draft pick compensation that Parsons would demand in trade. The likelihood of him leaving Dallas is not too low though - Jerry may feel that money is better spent on helping his offense and drafting for defense.