The Serbia striker's current deal is running down this season, with an expectation that he will be leaving this summer.
But Di Livio is convinced coach Luciano Spalletti can help Vlahovic return to his best form.
He told TMW: "I hear a lot of people talking about the lack of a striker. But in my opinion, signing a striker just for the sake of signing one would have been a mistake.
"It would have been better to do nothing except bring in (Jeremie) Boga. Especially since we have one at home...
"Yes, Vlahovic needs to be evaluated: with Spalletti, he can return to certain levels. I'd try to convince him. I correct myself: Juve doesn't have to convince anyone, it's the players who have to convince themselves.
"But I think with Luciano, he can return to his best, that's all.
"Given the way he celebrated the other night, I think he's very committed to Juventus. I really liked him. Clearly, he can't expect to continue earning the same salary."
Spalletti's deal also expires in June and Di Livio added, "He needs to be reappointed immediately, he needs to be secured. We need to work immediately on the future Juventus, listening to Spalletti."