As reported by Tuttosport, Massimiliano Allegri is looking to follow up the recent acquasition of Cristiano Ronaldo with the signing of the experienced Uruguayan, amid uncertainty regarding a number of the club's current centre backs.
Despite the return of Mattia Caldara after a loan spell at Atalanta, Juventus have already lost Benedikt Howedes after he returned to Schalke following his loan stint in Turin, while the futures of Medhi Benatia and Daniele Rugani are far from clear, with the latter reportedly close to a £40m deal with Chelsea.
As a result, Allegri is hoping to persuade Godin to leave the Spanish capital and join the reigning Serie A champions, as they look to mount a serious challenge on next season's Champions League.
The 32-year-old is regarded as one of the world's best centre backs, helping Atletico Madrid to a La Liga title, Copa Del Rey, two Europa League titles and two Champions League finals since his arrival in 2010.
Godin's contract at the Wanda Metropolitano expires at the end of next season, although as his recent performances for Uruguay in the World Cup suggests, Diego Simeone will be desperate to keep hold of the defender.
Juventus are rumoured to be keeping tabs on a number of centre backs throughout the course of the transfer window, with Godin's teammate Stefan Savic also a target for the Turin-based club, while Arsenal's Shkodran Mustafi has also emerged as a shock alternative should Juve fail to land Godin.