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The 31-year-old attacking midfielder will be a free agent in summer and Brendan Rodgers wants to snap him up.
The Leicester City boss brought him to Liverpool as well and the two share a good working relationship.
As per Sky Sports, the Foxes have made an initial approach for the midfielder. Rob Dorsett from Sky Sports has confirmed that Brendan Rodgers wants Lallana to know that he is a key target for the Foxes.