That will pave the way for his possible return to the New York Rangers if the NHL club does indeed put in a claim for him.
The Rangers allowed Avery to resume his career with their AHL affiliate in Hartford, Conn., earlier this month.
Any of the 29 NHL teams could put in a claim on Avery and owe him half of his remaining contract. He must be on an NHL team's roster by the trade deadline Wednesday to be eligible for the playoffs.
Avery was suspended six games by the NHL in December for making a crude remark about other hockey players dating his former girlfriends.
He completed a two-month treatment in a league counseling program before clearing normal NHL waivers earlier this month and being loaned to Hartford.
The 28-year-old player spent parts of two seasons in New York before signing a $15.5 million, four-year deal with Dallas. The Stars have said repeatedly Avery won't return to their team.
Avery is earning $3.5 million this season and has three more years left on the deal that pays him $4 million a season.
In Avery's season and a half with the Rangers, the club was 50-23-13 when he played and 24-35-9 when he was out of the lineup.
Pierre LeBrun covers the NHL for ESPN.com.