The Jags would have to take a 33mil cap hit, which they cant afford, to cut him before June 1st (only 20 mil cap hit if jut after that). Jags have Minshew on a cheap rookie contract, so getting cap space to fill out their roster and help him out is important. They probably would give up nice compensation for another team to take on the contract. Maybe throwing in a guy like Riley Ridley, on a rookie comtract, can sweeten the deal and get better compensation.
But as much as I like the idea of receiving a draft pick for a once competent QB, it doesnt make sense for the Bears to make this happen. We will probably be able to sign a guy like Mariota for 7-10 mil a year. We could then use the money to extend guys like Eddie Jackson, Robinson, Trevathan, maybe Skrine (to replace Prince) etc..