On-loan from Napoli, Osimhen can leave the Azzurri this summer for a set fee of €75m. However, the buyout clause does not apply to local Italian rivals.
Il Corriere dello Sport says Juve management aim to trump foreign rivals by tabling an offer of €85m to Napoli for the Nigeria international.
For his part, Napoli president Aurelio de Laurentiis would be prepared to sell for such a figure, though much will depend on Osimhen.
Given the clause in his contract, Osimhen can still leave for €10m less than what Juve are willing to pay. However, the free-scoring striker remains open to staying in Italy.
Also watching developments are Saudi Pro League club, Al-Hilal, which are willing to meet the clause and pay Osimhen a massive €30-35m-a-year to move to the Middle East.