Teams have 24 hours to put in a claim for Haynesworth, a two-time Pro Bowler, who was traded to the Patriots before the start of the season by the Washington Redskins.
Haynesworth, 30, has failed to produce the form that made him a standout on the defensive line in seven seasons with the Tennessee Titans before his trade to Washington for the 2009 season.
The beefy defensive tackle had reported out of shape to Washington and was at continual odds with the coaching staff there before being moved to New England.
Haynesworth clashed with Redskins coach Mike Shanahan a season after being signed to a $100 million free-agent contract by Washington's previous coaching-management regime.
(Reporting by Larry Fine in New York, Editing by Justin Palmer)