The Redskins are also reportedly bringing back veteran linebacker Mason Foster on a two-year deal.
The Redskins parted ways with quarterback Robert Griffin III on Monday.
McCoy's deal can be voided after two years, according to ESPN.com. He signed one-year deals each of the past two offseasons with Washington,
McCoy, 29, only attempted seven passes in 2015 and played in one game. McCoy has played in 35 career games with the Cleveland Browns, San Francisco 49ers and Redskins, throwing 26 touchdowns and 23 interceptions.
Foster, 27, was signed by the Redskins on Sept. 29 as a free agent following his September release by the Chicago Bears. He started five games and played in 13 regular-season games, finishing with 37 tackles and a fumble recovery. He also started in the wild-card loss to the Packers.
Foster spent his first four seasons with the Tampa Bay after being the Buccaneers' third-round pick in 2011. He started 54 games.
The Redskins also reportedly re-signed defensive lineman Kedric Golston to a one-year deal.
Golston, 32, has recorded 222 tackles with seven sacks, seven passes defensed and two fumbles forced in his career with Washington.