According to NFL Network's Ian Rapoport, the Redskins are "shopping" Jones and remain "likely" to draft a running back before the weekend is over.
Jones rotated in and out of Washington's backfield for seven games last season, but he finished the campaign in head coach Jay Gruden's doghouse; he ended the year with eight straight appearances on the inactive list.
Instead, Gruden opted to go with Rob Kelley, Chris Thompson—who recently re-signed with Washington on a one-year restricted free-agent tender—and Mack Brown.
Gruden has also been noticeably silent about a possible role for Jones moving forward.
According to CSN Mid Atlantic's Rich Tandler, Gruden "acknowledged that 2015 third-round pick Matt Jones is still on the roster, but he didn't have much good to say about him."
Conversely, Gruden praised Kelley at last month's league meetings in Phoenix, Arizona.
"Oh, man, I love Rob Kelley," he said, per Tandler. "I thought he played great. You throw a rookie free agent into the fire like that and see him play and compete. Not one time did I feel like it was too big for him. Not once. That's a hell of a thing to say for a kid out of Tulane who only had a couple of carries his senior year."
Jones, 24, is signed through the 2018 season and is scheduled to earn base salaries of $629,000 in 2017 and $719,000 in 2018, according to Spotrac.com.