Drewiske, 28, had one goal and three assists in 20 games for Los Angeles but had been a healthy scratch of late. He has four goals and 18 assists in 126 career NHL games.
The six-foot-two 220-pound native of Hudson, Wisc., was a member of the Kings' Stanley Cup team last spring but saw no action in the playoffs.
He is earning a pro-rated US$650,000 and can become an unrestricted free agent in the summer.
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