So if Burrow says no, does the nfl fully bar him from free agency? Can y’all fill us in on what leverage Burrow has?
If he sat out the year he would be a part of the 2021 draft where there is no guarantee that he would be the first pick. The threat of that worked for John Elway and Eli Manning but I hear that Bengals owner Mike Brown is so stubborn that he would call Burrow's bluff and let him sit.
He has next to no leverage. It's all public perception. Eli Manning had family money and clout to force the Chargers to trade him and it almost didn't happen. Had Ernie Accorsi not been so sold on Eli for the Giants he probably is a Charger. He might have legitimately sat out though. We will never know. Elway had the threat of playing pro baseball to aid his threat and force a trade. Burrow can publicly and privately tell the Bengals that he won't play for them. They would still own his player rights if they draft him. His only recourse then would be to hold out. If he did not sign and held out the entire year he'd go back into the next NFL draft. The Bengals would lose his rights and would have wasted their pick on him. But Joe would be costing himself a year of huge money and potentially hurt his draft stock the next year and he'd not play for a year? No guarantee he'd go first overall next year. He's got very little leverage truly other than public perception. Edit: In fact, he'd probably have a better chance to force a trade by publically being quiet and privately yelling at the Bengals he won't sign which would give them a chance to get the largest compensation in a trade. If he's publically saying he won't go to Cincy then the team trying to trade for him can offer less because they weaken the Bengals trade leverage.
Colin Cowherd goes off https://www.foxsports.com/watch/the-herd-with-colin-cowherd/video/1697581123754
I doubt the Bengals want to lose their first round pick, so he has some leverage. It would be a risk, but getting paid less on a good team would be a long term investment.