Poole previously visited with the Jets and reportedly had interest from the Bengals.
The Jets could view Poole as a replacement for Buster Skrine as their slot corner.
Poole, 26, wound up signing on with the Falcons as an undrafted free agent out of Florida back in 2016. He has managed to make the 53-man roster in all three of his seasons.
Poole was in line to be a restricted free agent this offseason, but the Falcons declined to tender him a contract.
In 2018, Poole appeared in all 16 games for the Falcons and recorded 74 tackles, three sacks, three interceptions and two fumble recoveries. Pro Football Focus has him rated as the No. 81 cornerback out of 110 qualifying players.