Secured at Inter until 2024, the Nerazzurri are willing to up his terms given the impact he has made over the last two years with the Serie A title holders.
Klopp is convinced by the talent and potential of the Italy Euro 2020 winner and the Reds have registered their interest with Barella's management team this season.
For their part, Inter are insisting they're no longer under pressure to sell their stars, though the financial situation of owners Suning remains a concern.
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