Gresham, a former first-round pick, spent the first five years of his career with the Cincinnati Bengals. The team decided not to pursue a second contract with the 27-year-old, who underwent surgery to repair a herniated disc this offseason. Gresham's health status remains unclear. He met with the Arizona Cardinals this week, though the team did not sign him.
The Packers' interest in Gresham could be influenced by the recent legal troubles for Andrew Quarless. The veteran tight end was arrested earlier this month for discharging a firearm in Miami. The league has yet to punish Quarless for the incident, though a suspension could materialize in the coming weeks.
Gresham caught 62 passes for 460 yards and five touchdowns last season. For his career, the tight end has compiled 280 receptions, 2,722 yards and 24 touchdowns.