A league person with firsthand knowledge of the situation told The Associated Press that Avery has completed a counseling program under the NHL/NHLPA behavioral health program and was placed on Dallas' active roster. The Stars then placed Avery on waivers.
The person spoke on condition of anonymity because the move had not been announced.
Avery must clear waivers by Monday. A team could claim him before then, but would have to pay the remainder of the four-year, $15.5 million contract he signed this summer.
The New York Post reported Friday that the New York Rangers have had discussions about the possibility of bringing back Avery, who played with the team for a season and a half before signing with Dallas.
Officials from the Stars and Rangers declined to comment on the report Friday.
Avery's stay with the Stars ended when he made crude comments to reporters about former girlfriends before a game at Calgary on Dec. 2. Already unpopular with teammates and coaches, Avery was suspended for six games by the NHL and then entered a counseling program.
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Stars officials and players have said they don't want Avery back under any circumstances. With their 10-2 victory over the Rangers on Friday night, the Stars improved to 17-7-3 since Avery last played in a Dallas uniform.
For Avery to be eligible for the playoffs, a team would have to pick him up before the March 4 trade deadline.
Avery's possible return to the NHL still involves several steps.
After clearing waivers, he would be assigned to an American Hockey League team for a conditioning stint. The Stars do not have an AHL affiliate, so they would have to find a team willing to take him. The Rangers' affiliate in Hartford, Conn., could be an option.
Any team could claim him off waivers before the assignment, but would have to pay his full contract. If Avery clears and spends time in the AHL, he would have to clear waivers again before coming back to the NHL. Any team could then claim him for half his remaining contract.