Il Corriere dello Sport says after their attempt in January, Inter have not dropped their interest in the Scouser.
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The Italian giants are expected to make another attempt to sign Jones in the summer transfer window.
Jones' contract with Liverpool runs until the summer of 2027.
This summer there is only one year left on the contract, and Inter hopes that this fact will lead Liverpool to being more reasonable about his price.
This season, Jones has registered one assist in 24 appearances in the Premier League.