If another NHL team doesn't claim him within 24 hours of being placed on waivers, the Rangers can send the controversial forward to their affiliate in Hartford.
Avery was claimed off waivers by New York from Dallas on March 3, 2009. The Stars signed him to a four-year, $15.5 million deal in 2008.
According to NHL.com, Rangers head coach John Tortorella said he wanted to have just one extra forward on the roster, with the spot coming down to Avery and Erik Christensen.
Avery, 31, recorded three goals, 21 assists and 174 penalty minutes in 76 games last season.