Grant, who was in Chicago for a workout with the Bears, reportedly flew to Washington on Tuesday evening to be with the team.
Grant was released by the Green Bay Packers following the 2011 season, in which he rushed for 559 yards on 134 carries.
He suffered a season-ending injury in Week 1 of the 2010 season following consecutive 1,200-yard campaigns.
UPDATE: Grant later tweeted out that he was on the Redskins and thanked the fans in Green Bay.
Big Thanks to all the Packer fans for all the support. Great 5 years.. Looking forward to the next journey. With that said Go Skins #HTTRâ Ryan Grant (@RyanGrant25) September 26, 2012