The Patriots are in need of some help at both positions, but tight stands out as a need right now.
Leggett, 25, is a former fifth-round pick of the Jets back in 2017. New York waived him shortly after the 2019 NFL Draft and he was later claimed off of waivers by the Buccaneers.
Leggett was in the third year of his four-year, $2,682,052 contract and set to make a base salary of $645,000 for the 2019 season when the Bucs waived him coming out of the preseason. He was on and off their practice squad before recently being cut loose.
In 2018, Leggett appeared in 15 games for the Jets and caught 14 passes for 114 yards receiving and one touchdown.