The 31-year-old forward was informed Tuesday that he would not be on the postseason roster of the AHL's Connecticut Whale, the Rangers minor league affiliate, and was told he no longer needed to report to the rink for practice or games, according to a Rangers spokesperson.
Avery declined to comment when reached via email by ESPNNewYork.com on Tuesday night.
Waived twice by the Rangers this season, Avery was scratched indefinitely in his second stint with the Whale in Hartford. He last appeared in a game for them on Jan. 27.
Avery is in the final year of a $15.5 million, four-year contract.
Katie Strang covers the NHL for ESPNNewYork.com. Information from The Associated Press was used in this report.