The Argentina striker is off contract in June and talks over a new deal have stalled.
Klopp, reports TMW, is a big fan of Dybala and wants Liverpool to explore the prospect of bringing him to England.
The Reds are free to secure Dybala to a pre-contract, while Juve have informed his camp they intend to make a new offer in February.
Inter Milan are also interested in the striker.
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