The Serie A side are not yet done bolstering their squad and have reportedly set their sights on the Portuguese defender, who has been a core piece at the Russian club
The Italian club are believed to be keen on strengthening their defensive resources as they look to mount a serious challenge in Serie A.
Alves joined Zenit from Porto last summer for a fee of €22 million and has been an ever-present figure at the Estadio do Dragao since his arrival.
Juventus coach Antonio Conte is understood to be an avid fan of the Portuguese defender and to have made him a priority in the last week of the transfer window.
In order to convince Zenit to part company with the Portugal international, Juventus will reportedly include in the deal Simone Pepe and Leonardo Bonucci, both of whom have been linked with the Russian side earlier in the summer.