Graham, 25, was a third-round pick of the Bills back in 2012. However, he lasted just two years with the team before Buffalo placed him on waivers about a month ago as they trimmed their roster down to 53 players.
The Tennessee Titans later claimed him off of waivers, but he was once again cut a few days ago to make room for TE Chase Coffman.
Last year, he appeared in all 16 games for the Bills and caught 23 passes for 361 yards receiving and two touchdowns.
We’ll have to see if the Jets sign him to a contract this weekend or early next week.