The Patriots currently have just four running backs on their roster -- James White, Dion Lewis, D.J. Foster and Rex Burkhead -- as LeGarrette Blount and Brandon Bolden are unrestricted free agents. That doesn't include fullbacks James Develin and Glenn Gronkowski.
This year's draft class is considered strong at running back, so the Patriots could focus on supplementing the position that way. Last week, for example, Bill Belichick spent time at the University of Tennessee with running back Alvin Kamara as part of his standard scouting process. The Patriots will thoroughly scout all running backs.
As for the 6-foot, 220-pound Gaffney, he first joined the Patriots in July of 2014 after he was waived by the Carolina Panthers. He spent his first two NFL seasons on injured reserve and spent half of 2016 on the team's practice squad. Belichick has praised Gaffney's work ethic multiple times in recent years.
The Stanford alum entered the NFL as a sixth-round draft choice of the Panthers in 2014.