The move comes as Forest manager Nuno Espirito Santo seeks to strengthen his full-back positions, which have been a concern for the team throughout the summer.
According to transfer reports, the deal is expected to be worth over €15 million, with the two clubs currently exchanging paperwork ahead of a medical.
Savona, who is 22 years old, is a versatile defender capable of playing across various positions in the backline.
He made 40 appearances for Juventus in all competitions last season, showcasing his skills and experience.