The Argentine has lost his first-choice with Juve this season.
Corriere dello Sport says he is ready to consider his future in the summer if things don't change and that has alerted Liverpool.
The Reds want to add a new central striking option to lift some of the burden off Roberto Firmino and Dybala certainly fits the bill.
Liverpool could even make a move for the 25-year-old before the end of the season - but he will not come cheap.
Juve would look for around €120m (£103m) for the forward.