Price, whose playoff heroics were an essential factor in Montreal reaching the Stanley Cup Final this season, is in the fourth year of an eight-year contract that carries an annual cap hit of $10.5 million.
During Montreal's run to the Cup Final, Price started all 22 games. The 33-year-old registered a sterling 2.28 goals-against average and .924 save percentage, as well as one shutout. In the regular season, Price appeared in 25 games, going 12-7-5 with a 2.64 goals-against average and .901 save percentage.
Price waiving his no-move clause would allow the Canadiens to protect Jake Allen during the expansion draft, while banking on Price's salary deterring the Kraken from claiming him. He is also owed an $11-million signing bonus in September.
Allen, who signed with Montreal last off-season, posted an 11-12-5 record with a 2.68 goals-against average and .907 save percentage during his debut Canadiens campaign.
Uncertainty over whether or not Price will play for Montreal next season marks the latest surprising turn in an eventful off-season for the Canadiens.
Shortly after extending Dominique Ducharme, the team's head coach who helped engineer Montreal's return to the Final for the first time since 1993, news broke that team captain Shea Weber's career was being threatened by lingering foot and ankle problems.
The expansion draft takes place next Wednesday at 8 p.m. ET, and can be seen live on Sportsnet.