Plus the Saints are already already something like $65M over the cap.

They excel at creative bookkeeping, but even if they signed Rodgers to a 3 year/$90M deal structured such that the cap hits went $11M, $31M, $36M, $6M, $6M (using voidable years) that would push them $75M over the cap.

So if they signed Rodgers to that deal, and then converted the entire base salaries of Michael Thomas, Cam Jordan, Taysom Hill, Ryan Ramcyzk, Andrus Peat, Marshon Lattimore, Marcus Davenport, and Malcom Jenkins all into bonuses spread over multiple voidable years, and cut Bradley Roby, then they'd have enough to fit Rodgers under that deal and fill out the rest of the roster with minimum salary players.

But they also want to resign Terron Armstead. So they'd have to push even more off into future seasons. And already they're creating major issues. For example Michael Thomas would then have a $29M cap hit in 2023. Trading him or cutting him then would still be something like $15M in dead money.