In addition to offense, Barner also has a lot of experience returning punts, which the team needs help with after releasing Riley McCarron. He did not make the final roster and went unclaimed on waivers.
Coleman visited with the Patriots on Monday and was scheduled to take a trip to Philadelphia Tuesday.
Tate, selected by the Patriots in the third round of the 2009 National Football League draft, spent his last two seasons with the Bills serving primarily as a kick and punt returner.
The 24-year-old played in 19 games with the Browns but injuries meant he missed significant time.
He has 56 career receptions for 718 yards and five touchdowns. With Julian Edelman still suspended, New England has rolled with a thin receiver group, consisting of Phillip Dorsett, Chris Hogan and Cordarrelle Patterson.
The Michigan State product spent his first three seasons in the National Football League with the Denver Broncos.
Barner, 29, was originally drafted by the Carolina Panthers in the sixth round (182nd overall) of the 2013 NFL Draft out of Oregon.
The 6-foot-1, 212-pound Fowler had 56 catches for 698 yards and five touchdowns from 2015 to 2017 with the Broncos. He spent the last three seasons with the Eagles, where he totaled 310 rushing yards and three touchdowns on 71 attempts across 36 games (one start).