On Monday, coach Jay Gruden said that McCoy would start against Dallas unless Griffin is "100 percent," but did not rule out Griffin playing.
Griffin has not played since dislocating his ankle during a Week 2 win over Jacksonville. There was no fracture and the quarterback did not require surgery.
Cousins took over for Griffin against the Jaguars and started the next five games, throwing for 1,710 yards, 10 touchdowns and nine interceptions, including a four-interception game against the New York Giants.
Cousins was benched during Washington's game against the Tennessee Titans on Sunday. McCoy replaced him at the start of the fourth quarter and completed 11-of-12 passes for 128 yards and a touchdown in a 19-17 win.
McCoy is a former third-round pick out of Texas. He spent last season as a backup for the 49ers, throwing one pass. Prior to that he was in Cleveland.
- Molly Geary