Brown is in his fifth season as the Redskins director of pro personnel, where he oversees opponent scouting, player evaluation and draft decisions.
He was hired by Washington in 2008 after serving as the assistant director of pro personnel with the Chicago Bears from 2001-07. Brown graduated from North Carolina State in 1999, and immediately entered the NFL as a scouting intern with the Indianapolis Colts in 2000.
The Cardinals fired Graves and head coach Ken Whisenhunt on Monday. Graves had been with the organization for 16 years, serving the past nine leading all football operations.
Current Arizona director of player personnel Steve Keim is reportedly in the mix to take the general manager position, according to The Arizona Republic's Kent Somers.