Hunter previously visited with the Patriots while Elliott recently met with the Bills.
Hunter, 26, was taken with the No. 34 overall pick by the Titans back in 2013. The Titans elected to cut him loose last year, but he was later claimed off of waivers by the Dolphins. Hunter agreed to a pay cut to remain with the Dolphins before he was once again placed on waivers.
Hunter was later claimed by the Bills claimed a few weeks into the 2016 season.
Hunter played out the in the final year of his four-year, $5.424 million rookie contract and is now testing the open market for the first time in his career.
In 2016, Hunter appeared in 13 games and caught 10 passes for 189 yards receiving and four touchdowns.