Liverpool released its 20-man traveling squad for the tournament on Sunday, omitting Lovren and three youth stars from the provisional roster.
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Liverpool will meet Monterrey on Wednesday in the Club World Cup semifinal, with the winner meeting either Flamengo or Al-Hilal on Saturday.
CONCACAF Champions League winners Monterrey advanced to the semi on Saturday, getting a world class strike from Leonel Vangioni in the 3-2 win.
Liga MX has never put a team in the Club World Cup Final.
Liverpool lost the 2005 CWC Final to Sao Paulo in Japan, one of three PL teams to contest the final. Chelsea lost in 2012 after Manchester United won the 2009 crown.
European sides have won 10 of the last 11 finals.