Reports from Calciomercato link the 33-year-old with a move back to Serie A, where he played for Roma before joining Liverpool for a then world-record fee in 2018.
The connection with the Juventus dugout is personal.
Manager Luciano Spalletti worked with Alisson during their time together at Roma and is said to have identified him as a prime target. That prior relationship could prove significant in any negotiations.
Juventus want to move on from current goalkeeper Michele Di Gregorio this summer, while back-up Mattia Perin will be entering the final year of his deal. The position needs a high-profile overhaul.
Alisson has been considered alongside Tottenham Hotspur's Guglielmo Vicario and Atalanta's Marco Carnesecchi. But according to Calciomercato and Corriere dello Sport, the Liverpool goalkeeper represents the most cost-effective route.
Liverpool triggered a one-year contract extension earlier this month, keeping Alisson under contract until June 2027. That means any deal this summer would require a transfer fee — reports suggest Liverpool would seek €15-20 million — plus a salary of around €8 million per year.
The stumbling block is the player himself.
Fabrizio Romano reports that Alisson's position is clear: he wants to fulfil his contract at Liverpool and stay for one more season. Liverpool, for their part, have sent a strong message to interested clubs that he is not available this summer.
Giorgi Mamardashvili, signed from Valencia last summer for £29 million, remains in the wings. The Georgian has played just 934 minutes compared to Alisson's 2,486, but Liverpool face a decision about the goalkeeping transition sooner rather than later.
For Juventus, the door remains ajar. Whether Liverpool will open it this summer is another matter.