The veteran is leaving Real Madrid after 10 years as a senior player with the Los Merengues.
Now a free agent, Vazquez has offers from across the world, including from the Middle East and Turkey.
However, Tuttosport says Juve are also keen, where they see Vazquez as a readymade replacement for Marseille and Nottingham Forest target Timothy Weah.
Along with the 34 year-old, Juve are also interested in Almeria wing-back Marc Pubill.