The Argentinean player previously revealed his intention of sealing a move to a better club in the close season, while recent reports linked him with Serie A sides Inter Milan and Fiorentina.
According to D'Ippolito, Juventus are closing in on his client, after they failed to sign Udinese's Gaetano D'Agostino.
"I give it as certain that Cristian won't be at Lazio next year," he told the Italian press.
"We have talked with Juventus but the Bianconeri are still deciding what to do with D'Agostino, after which if they give up on the Udinese midfielder they will think about Ledesma."
Moreover, the agent assured that AC Milan could also be in the hunt for Ledesma in case Andrea Pirlo joined Chelsea as incessantly reported.
"We don't care about being second choice also because we are still in contact with another club of the same level as Juve who want Cristian. I'm talking about Milan," D'Ippolito added.
"At Milan it's clear that if Pirlo leaves the first choice is Ledesma, so Cristian will go to either Juve or Milan.
"At this point we have to wait for some developments in the market linked to Milan and Juve, but about the future of the player I have only one certainty and I'll repeat it, that he won't play any more at Lazio."