"I just don't think playing on the practice squad is reflective or indicative of my career," Reid said Tuesday, according to Rob Maaddi of Associated Press.
"I'm just not in a place to play on the practice squad right now ... If they go a different direction, I'll be ready."
Reid was released by the Carolina Panthers in March after two seasons and has yet to join a team for the 2020 campaign.
The 28-year-old started in all 29 games he played for the Panthers, who were then coached by current Washington head coach Ron Rivera. Reid accumulated 147 tackles, five sacks, one interception, and 11 pass breakups with Carolina.
Reid has been one of the most outspoken figures in the NFL regarding social issues in the U.S. He was the first player to join quarterback Colin Kaepernick's protests during the national anthem when they were teammates on the San Francisco 49ers from 2013-16.
Washington's secondary took a big hit last week after losing former Pro-Bowl safety Landon Collins for the remainder of the season to an Achilles injury.