The Serbian international revived his career by joining German side, Schalke 04, in January after being frozen out at Manchester City.
According to Tuttosport, Juventus have offered a deal to the German club that would see the centre-back initially join Juve on loan for a year, with the option to buy the player outright thereafter.
Schalke are looking to sell Nastasic for an upfront fee of €13 million, but a compromise could be reached given the German side’s eagerness to let the Serbian international leave the club in order to raise funds.
Natasic enjoyed an excellent spell in Serie A with Fiorentina during the 2011/12 season which earned him a move to Manchester City for €15 million plus Stefan Savic.
He had a successful first season with the Citizens but subsequently struggled following an injury-ravaged campaign in 2013/14.
The Bianconeri are looking at the 22-year-old as a potential replacement for Angelo Ogbonna who is reportedly close to joining West Ham United.