NFL Network's Ian Rapoport cited sources saying that Charles will visit the club's brass while Darkwa will work out for the Redskins.
The Redskins have been besieged by injury at the position, including rookie Derrius Guice. The promising second-round pick was lost for the season because of a torn ACL sustained in the preseason opener against the New England Patriots.
The latest injury to a running back is undrafted rookie Martez Carter, who has suffered from hamstring problems in the preseason. He played Thursday against the New York Jets and led the Redskins with 45 yards rushing -- including a 30-yard run -- on seven carries.
Fellow running backs Samaje Perine and Byron Marshall left the game versus the Jets because of ankle injuries. The Redskins now have only three healthy running backs in Rob Kelley, Chris Thompson and Kapri Bibbs.
Charles will be visiting the club following nine seasons in Kansas City and one with Denver in 2017. The 31-year-old Charles had 69 carries for 296 yards to go along with 23 receptions for 129 receiving yards last season with the Broncos.
A four-time Pro Bowl selection, Charles was released by Kansas City in February 2017 after becoming the Chiefs' career rushing leader.
Darkwa compiled 1,038 rushing yards and nine rushing touchdowns with the New York Giants. In 2017, the 26-year-old carried 171 times for 751 yards -- a 4.4-yard average -- and five touchdowns.