The 5-foot-10, 210-pound Burkhead entered the NFL as a sixth-round draft choice out of Nebraska, and could be eyed to fill Brandon Bolden's role in New England as a reserve running back and special teamer.
Burkhead had 74 carries for 344 yards and two touchdowns and 17 receptions for 145 yards last season. He played 22 percent of the team's offensive snaps in 2016 and 47 percent of the special teams snaps.
Burkhead, who turns 27 on July 2, was primarily a special teamer in his first three NFL seasons before injuries to Jeremy Hill and Giovani Bernard opened up opportunities for him on offense last season.
"I'm confident in my skills, I know what I can do, just needed an opportunity,” Burkhead said last season, according to the Cincinnati Enquirer. "For me, it came year four into the NFL, so I've been patiently waiting for it and just did my best out there when I got the chance. ...
"I love it here in Cincinnati, I hope I can stay here,” Burkhead said at the time.
At running back, the Patriots have Dion Lewis, James White, D.J. Foster and Tyler Gaffney under contract for 2017, while LeGarrette Blount and Bolden are unrestricted free agents. Lewis and White are scheduled for unrestricted free agency after the 2017 season.