This opens up a 21-day window for the two to practice with the team before returning to the active roster.
Davis, 24, was a four-year starter at California and was a finalist for the Burlsworth Trophy before the Jets selected him with the No. 68 pick in the 2020 draft.
He signed a four-year $4,917,384 rookie contract that included a $1,136,280 signing bonus.
In 2020, Davis appeared in 10 games for the Jets and recorded 36 total tackles, one fumble recovery and one pass defense.
Neasman, 29, wound up signing on with the Falcons as an undrafted free agent out of Florida Atlantic back in 2016. He was cut loose at the start of the 2016 season and later signed to the Falcons practice squad.
The Falcons declined to tender him a qualifying offer in 2018 and he later signed on with the Saints. Neasman returned to the Falcons in 2019 and agreed to a one-year contract for the 2020 season.
In 2020, Neasman appeared in all 16 games for the Falcons and recorded 24 tackles, one sack and no interceptions.