The Tigers dismissed Green-Beckham after he was implicated in an assault investigation into an April altercation involving Green-Beckham, his girlfriend and two other women.
The incident was the latest in a series of indiscretions involving Green-Beckham at Missouri.
Oklahoma announced Green-Beckham's transfer last month.
To appeal for Green-Beckham's immediate eligibility, the school reportedly will use the so-called "run-off" waiver, which applies to athletes dismissed from their programs for reasons they can't control.
According to the report, Oklahoma will argue that Green-Beckham was not charged in the altercation that led to his dismissal from Missouri. The school has yet to file the waiver.
If Green-Beckham is not granted the waiver, he must sit out the upcoming season in accordance with NCAA transfer rules.
Green-Beckham caught 59 passes for 883 yards and 12 touchdowns in 2013. The Springfield, Mo., native was the top-ranked prospect in the class of 2012.
- Chris Johnson