The Japan international impressed for Parma in Serie A last season and further raised his profile at the 2026 World Cup in the United States, Canada and Mexico.
Suzuki's involvement ended with Japan's last-gasp elimination at the hands of Carlo Ancelotti's Brazil. He is now free to focus on his next club move, which is not expected to keep him at the Stadio Tardini.
Parma have set an asking price of €30 million including bonuses for the 23-year-old.
Leeds United have long been considered favourites to land Suzuki, with Aston Villa potentially opting to keep Emiliano Martinez instead.
No agreement has been reached yet, however, and Sportitalia claim Juventus have made an approach to ask about the conditions of a potential transfer.
A move to Turin would follow in the footsteps of Gianluigi Buffon, who also moved from Parma to Juventus. Suzuki will turn 24 next month.
He was born in the United States to a Ghanaian father and Japanese mother but grew up in Japan and represents the country at international level.
Parma signed Suzuki from Belgian side Sint-Truiden in 2024, paying €8.2 million plus add-ons and a ten per cent cut of any future sale fee.
Juventus's interest adds a fresh name to a goalkeeper market already being shaped by Leeds and Aston Villa's search for a long-term successor to Martinez.
Suzuki's stock has risen sharply since his World Cup displays, and Parma will hope competition between multiple suitors drives the fee closer to their valuation.