A former University of Miami standout who was drafted in the first round by the New England Patriots, Meriweather started four games last season for Chicago and registered 32 tackles. Three years ago, Meriweather intercepted five passes and posted 83 tackles.
For his career, he has 293 tackles, two sacks, 12 interceptions and five forced fumbles.
Meriweather is a hard hitter, but has drawn fines from the NFL for his head-hunting approach to the game.
The Redskins aren't inclined to hold onto oft-injured free agent safety LaRon Landry, who is scheduled to visit the New England Patriots on Friday.
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Brandon Meriweather to Redskins
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