Waiver Priority based on current league standings (potential OBJ waiver)

Saints do not have the cap room to claim him. They would have to hope he clears waivers.
Looks like Beckham’s restructured contract only costs $1 million against the cap. Now it’s a matter of do other teams view him as a necessary addition so he can fall down the waiver order and be claimed at 23rd by the Saints

https://saintswire.usatoday.com/2021/11/05/saints-sign-odell-beckham-jr-browns-nfl-waiver-order/The Browns announced Friday that they released Beckham, who must test the waiver wire like every other vested veteran across the league after the annual trade deadline passes. And his restructured contract means any team that claims him will have to count right around $1 million, per ESPN’s Jeremy Fowler. That’s affordable for just about every team in the NFL including the cash-strapped Saints once you factor in the cost of adding him (which would push another contract off their books). New Orleans is under the cap by $1,098,472, per ESPN’s Field Yates, but that number would change by Beckham’s contract replacing a bottom-of-the-depth chart player like Montravius Adams (saving $802,778) or Jalyn Holmes ($715,556).