There are too many other players to pay
The Saints have a TON of high-value players on the roster. We have seen that by the consecutive years they have made it to the playoffs. Unfortunately for Kamara, the Saints also have other players to think about when spending their money.
In 2021, the Saints are also going to have to pay Demario Davis, Jameis Winston, and Sheldon Rankins.
In 2022, the team is going to have to pay Ryan Ramczyk, Marshon Lattimore, Marcus Davenport, and Emmanuel Sanders. They also might have to pay Drew Brees again although that seems more and more unlikely.
They also already overpaid for Taysom Hill so they are going to have to eat that money over the next two years. All that to say, the Saints are not made of money and the cap space is limited, it may even decrease in the coming years.
Kamara might be a casualty of that number.
I am in no way saying that I do not want Alvin Kamara on the Saints for years to come. I am just saying that the Saints will be smarter with their money than to overpay for him. They will offer a valuable contract and the ball will be in his court.