Are you assuming he'd just keep his existing contract?
That's the whole point of him telling everyone he wants to play for the Jets or Saints. That means to the other 29 teams, if you trade for me, I will not sign any extension/restructure so you'll have to pay me $25M (or whatever it is) for 2025 and in 2026. Any of those teams won't trade draft picks for a half-year rental. And no way they're paying that insane contract.
If it's the Jets or Saints, he and his agent probably have an extension already drawn up and proposed. Right now it's looking more like NO since Carr still has several good years left. Rodgers has looked terrible all year, and he's old af