The 26-year-old goalie, who was a restricted free agent, had a salary arbitration hearing in Toronto on Sunday.
Forsberg was traded to the Hurricanes from the Chicago Blackhawks with defenseman Gustav Forsling on June 24 for defenseman Calvin de Haan. He played for Rockford of the American Hockey League last season and was 10-16-4 with a 2.97 goals-against average and .908 save percentage in 35 games (30 starts) with the Blackhawks in 2017-18.
Selected by the Columbus Blue Jackets in the seventh round (No. 188) of the 2011 NHL Draft, Forsberg is 11-24-2 with a 3.21 GAA and .901 save percentage in 45 games (39 starts) with the Blackhawks and Blue Jackets.