Asiasi is vaccinated, so he can return after two consecutive negative tests 24 hours apart.
The Patriots announced they have released receiver Devin Smith, who signed to the New England practice squad Dec. 9 and later signed a futures contract.
Smith, 29, entered the league as a second-round choice of the Jets in 2015. He also has played for the Cowboys.
Outside linebacker Kyle Van Noy and offensive tackle Trent Brown are not yet cleared for practice as both landed on the active/physically unable to perform list Tuesday. The Patriots can remove them from PUP at any time this summer.
The Patriots worked out free agent offensive tackle Jerald Hawkins. Hawkins, a fourth-round choice of the Steelers in 2016, has appeared in 19 career games with one start.