Poole is the leading candidate to replace Buster Skrine as the Jets' nickel corner. After four seasons in that role, Skrine signed a free-agent contract with the Chicago Bears. The Jets didn't try to retain him. They also have no plans to re-sign starter Morris Claiborne.
Poole, whom the Atlanta Falcons wanted to bring back but not at the price of a low-level restricted free-agent tender, started 21 of 47 games, including nine last season, since entering the league as an undrafted free agent in 2016.
The team's primary nickel back during his three seasons in Atlanta, Poole, 26, had three interceptions, two fumble recoveries, three sacks and 75 tackles last season, when he made $630,000.
He also contributed on special teams, making three tackles in 2018.
ESPN's Vaughn McClure and Rich Cimini contributed to this report.