Beginning Tuesday, teams have through March 6 to designate the players they want to franchise or transition tag. The Redskins have tagged Cousins the past two seasons.
Although the Redskins recently traded for quarterback Alex Smith, they could place a franchise tag on Cousins to prevent him from becoming a free agent and then trade him to get value in return.
According to the Post, citing a person with knowledge of the situation, Cousins will file a grievance through the NFL players' union if the Redskins tag him.
Cousins, 29, may argue that the team is violating the collective bargaining agreement since it has no intention of negotiating a long-term deal with him or having him play under the $34.5 million franchise tag guaranteed this year.
The franchise tag is usually used by teams to buy time to continue contract talks in hopes of agreeing to a long-term deal. Tagged players have until 4 p.m. ET on July 16 to sign multi-year contracts or extensions.
It is unlikely the Redskins would negotiate a long-term deal with Cousins since they just traded for Smith and signed him to an extension that the team controls for the next five years.
The Redskins, coming off a 7-9 season, could tag Cousins to prevent him from becoming a free agent on March 14. However, the team cannot trade him until he signs the franchise tag. Also, $34.5 million would count against their salary cap until they trade him.
The Buffalo Bills, Cleveland Browns, Denver Broncos, Minnesota Vikings and New York Jets are among the teams interested in Cousins, who threw for 4,093 yards with 27 touchdowns and 13 interceptions last season. The Browns and Jets have the most money of those teams to spend in free agency.
Browns offensive tackle Joe Thomas has publicly lobbied for Cousins to come to Cleveland, which is coming off a 0-16 record and has won just one game the past two seasons. Cousins has said he wants to play for a team that has the best chance to contend.