The Bianconeri have already edged out the Reds in one transfer race this summer, poaching goalkeeper Michele Di Gregorio from Monza after the Italian's agent held talks with Arne Slot's side.
Both Liverpool and Juve are also rumoured to have taken a liking to Nice lynchpin Thuram, who is the son of ex-France defender Lilian Thuram and the brother of Inter Milan striker Marcus Thuram.
The 23-year-old has now entered the last 12 months of his contract with Nice, who have resigned themselves to selling him for a cut-price fee this summer in order to avoid losing him for nothing in 2025.
Liverpool were extensively linked with a swoop for Thuram last summer, and while speculation died down this time around, the Frenchman was still believed to have had admirers on Merseyside.
Juventus confirm Thuram arrival in Turin
However, Juventus moved quickly to conclude a deal with Nice, and the Old Lady have now confirmed Thuram's arrival in Turin as he prepares to finalise his move to Thiago Motta's side.
Juve posted a video on social media of Thuram exiting the airport and jumping in a taxi ahead of his medical, and it is only a matter of time before his signing is officially announced.
The Bianconeri are reportedly set to pay around €25m (£21.1m) including add-ons to sign the former Monaco prospect, who has agreed terms on a five-year contract at the Allianz Stadium.
Thuram departs Nice having registered nine goals and 12 assists in 167 matches for Les Aiglons, whom he joined on a free transfer in the summer of 2019, and he made his debut for the France national team in March 2023.
The midfielder was on course to be named in France's 2024 Olympics squad, but head coach Thierry Henry recently confirmed that he had been blocked from joining up by Juventus.
Thuram will become the third new arrival at Juventus this summer following the captures of Di Gregorio and Douglas Luiz, and his arrival could very well open the door for compatriot Paul Pogba to depart.
The ex-Manchester United man was banned for four years for doping back in February, but remains under contract until 2026, while Arthur Melo and Weston McKennie are also facing uncertain futures.
Liverpool to poach Adrien Rabiot as Thuram revenge?
Despite conceding defeat in the race for Thuram, Liverpool are still believed to be open to the right opportunity for a new defensive midfielder, especially with Wataru Endo already in his 30s.
While Juventus have won the Thuram race, Liverpool are thought to be one of a few sides interested in Adrien Rabiot, who is now officially a free agent after his previous Juventus deal expired in June.
Paris Saint-Germain's Manuel Ugarte and Napoli's Stanislav Lobotka have also been linked with the Reds, as has Atalanta BC midfielder Ederson, but claims that the latter is closing in on a Merseyside switch are wide of the mark.