The 26-year-old, who has a Russian mother and Nigerian father, was watched by Anfield scouts at the Africa Cup of Nations.
Odemwingie plays for Lokomotiv Moscow and had a successful spell at Lille.
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Watched: Osaze Peter Odemwingie in action for Nigeria during the African Cup of Nations
See the video of Odemwingie scoring twice for Lokomotiv Moscow against Atletico Madrid
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