Kovalchuk is likely to be scratched for the second straight game when the Kings host the Detroit Red Wings at Staples Center on Thursday (10:30 p.m. ET; ESPN+, FS-W, FS-D, NHL.TV). He is in the second season of a three-year, $18.75 million contract (average annual value $6.25 million).
The Kings signed Kovalchuk believing he would put them back into contention to win the Stanley Cup. Instead, Los Angeles finished last in the Western Conference last season.
Kovalchuk had 34 points (16 goals, 18 assists) in 64 games in his return to the NHL after playing the previous five seasons in the Kontinental Hockey League.
McLellan, who was hired as Kings coach April 16, said there would be a fresh start for Kovalchuk as long as he was willing to work.
Kovalchuk has nine points (three goals, six assists) in 17 games this season but has a Kings-worst minus-10 rating. He has three points (one goal, two assists) in his past 13 games.
The Kings (6-11-1), tied with the Minnesota Wild for last place in the conference, are also trying to find regular playing time for younger players.