Goal understands that the 21-year-old has emerged as a serious option for the Bianconeri, though his €60 million (£51.8m/$67.4m) release clause is likely to prove problematic for the Serie A champions.
Juventus sporting director Fabio Paratici has watched the defender on multiple occasions this season as he aims to maintain good relations with the player's agent, Jorge Mendes, and has been impressed by what he has seen.
Despite the price tag, Juve will continue to monitor the situation as they aim to bring in defensive cover during the summer transfer window.
With Andrea Barzagli set to retire at the end of the campaign and Martin Caceres likely to be allowed to leave, it is expected that Juventus will sign two centre-backs during pre-season to provide competition for Giorgio Chiellini and Leonardo Bonucci.
One of those is set to be Genoa's Cristian Romero, with a €30m (£25.9m/$33.7m) deal having already been agreed to bring the 21-year-old to the Allianz Stadium.
Romero, though, could be loaned back to Genoa for a season before joining up with the first-team squad in Turin given Juve also have Daniele Rugani on their books to provide defensive cover.
While the search for a second signing at centre-back has led the Scudetto winners to Dias, a number of other options have been considered.
Roma's Kostas Manolas possesses experience of both Serie A and the Champions League, but his €36m (£31m/£40.4m) release clause is believed to be an issue when it comes to signing the 27-year-old Greece international.
Juve had hoped to tempt Ajax captain Matthijs de Ligt to Turin, but with Barcelona accelerating their pursuit of the Dutch teenager it is understood that the Bianconeri are no longer in the race to sign one of the most hightly-rated defenders of his generation.
Form and fitness respectively saw Boateng and Umtiti ruled out as viable options given their asking prices while it is believed that Zinedine Zidane will block any sale of compatriot Varane despite the French World Cup winner reportedly keen to move on from Santiago Bernabeu.
Quite who will be managing Juventus next season remains to be seen, with meetings ongoing between current boss Massimiliano Allegri and chairman Andrea Agnelli regarding the former's future.
Juve's shock exit to Ajax in the quarter-finals of the Champions League despite the presence of Cristiano Ronaldo has raised questions regarding Allegri's suitability to take the club forward in Europe despite his success domestically.
Former Juventus boss Antonio Conte had been mooted as a potential replacement but is now in talks with Inter while Tottenham coach Mauricio Pochettino was reported as a target on Friday after leading Spurs to the Champions League final.