In my eyes, there are 6 teams I could see being interested in Green, not counting the Bengals potentially giving him an extension, as a Larry Fitzgerald type locker room leader for them, and because, let's face it, they aren't exactly a hot free agent destination.
1. New England- I know, everybody gets talked about to New England, but Green gives them what they need, a consistent threat on the outside with size. Green has played his entire career with Andy Dalton, its possible the upgrade to Tom Brady would thoroughly rejuvenate his career.
2. Green Bay- A few years ago, this would have been a pipe dream, but the Packers new front office, has been very aggressive in upgrading the roster, and in trades(though that has mostly been draft day deals) Rodgers has probably taken a step back, and can no longer make just anyone a star, so an addition like Green, especially when added to Adams, could give Green Bay its most dangerous WR combo in ages. They also have been somewhat obsessed with getting bigger targets, all 3 2018 rookie WR's are huge, Jimmy Graham, Jace Sternberger, they've been trying to get that physical presence, that is something Green could provide.
3. San Francisco- A surprise contender to many, the 49ers passing game is a little smoke and mirrors behind Kittle. Its possible Samuel and Pettis both become very good players, but they aren't there yet, and both could greatly benefit for Green's presence, both on and off the field. Green would give the 49ers their first true #1 WR in a long time. Worst case scenario, he'd be what Anquan Boldin was to the Harbaugh teams. Best case scenario, he looks rejuvenated leaving Cinci, and joining a Shanahan offense.
4. Buffalo- Another surprise playoff contender, the Bills have a deep threat in Brown, and a slot weapon in Beasley, but don't have that true #1. They also have a recent history of trading with the Bengals. This probably wouldn't be a spot fantasy owners(of Green or Brown) would be excited about, but it would go a long way toward making the Bills a more complete and dangerous offense.
5. Oakland- They have some extra draft picks, and need a true #1 WR. They also have an aggressive coach, who had big plans for Antonio Brown before that fell through, and much like New England, Green brings a lot of the positives on field that Brown does, but is a solid citizen. Raiders have also been better than expected, I bet most don't realize if the playoffs started today, that Oakland would be the #6 seed. They only have 2 losses and those were to KC and Minnesota, 2 likely playoff teams.
6. Seattle- This one is probably just a pipe dream, but I think Seattle would like to not have to depend on guys like Jaron Brown and David Moore. Will Dissly's injury hurts a lot, and they could use another weapon. They are probably more likely to target somebody a little lower profile(E.Sanders maybe? Sanu?) but pairing Green with Wilson, and having him as a mentor for Metcalf would be pretty exciting.
I'd say a 1st is probably the price for Green. He's still in the later stages of his prime in my opinion. He likely has 2 big years left in him, but his game should age well, as he wins with size, and know how. I don't see him as a guy who will fall off a cliff like Dez Bryant, more like a guy like Larry Fitzgerald, who may lose his big play ability, but will still find ways to win for years to come.
I also think he's a guy teams will want to sign to an extension if they trade for him. Maybe not a long one, but say a 3 year deal?