The Serbia striker's current deal is running down this season and it had been claimed Juve were prepared to see him leave this summer.
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However, TMW says Juve management have now moved to open talks about a new contract.
Juve's offer is for €6m-a-year plus bonuses. However, that falls short of Vlahovic's demands.
The centre-forward is happy to continue on his current wages of €8m-a-year plus bonuses, knowing he can earn more should he leave for England.
Juve management are pushing Vlahovic to accept the cut as they want to establish a new wage ceiling set at €7m-a-year.