Off contract in June, Dybala is free to sign a pre-contract with any foreign club ahead of leaving Juve for nothing at the end of the season.
La Gazzetta dello Sport says City have come forward and tabled a deal worth €10m-a-year plus bonuses to 2026.
City's offer is the best Dybala has on the table.
Juve's last offer was for €7m-a-year plus bonuses to 2025.
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