Laine received a qualifying offer from Winnipeg on Tuesday.
Laine will bow out of the 2019 IIHF World Championship, Sara Orlesky of TSN.ca reports.
Laine scored a goal and added a power-play assist and three hits in Sunday's 6-3 win over the Blues in Game 3 of their first-round series.
Laine scored a goal in Wednesday's 2-1 loss to the Blues in Game 1 of the best-of-seven series.
Laine found the back of the net in Monday's 5-2 loss to the Stars.
Laine grabbed an assist in Saturday's clash with Nashville.
Laine picked up an assist in Friday's 8-1 win over the Hurricanes.
Laine snagged a power-play assist in Tuesday's 5-2 loss to Tampa Bay.
Laine tallied a helper in Sunday's 5-2 victory over Columbus.
Laine is now goalless in 12 straight games after being held off the scoresheet versus the Rangers on Tuesday.