The fullback has already seen a €12m bid from Forest turned down this summer.
However, Juve expect Forest to try again and have set their asking price at €18-20m.
TMW says Forest intend to return with a new offer of €15m plus a sell-on clause set at 10-15 per cent.
Wolves are also interested, but Forest are now regarded as favourites to land Savona, who is open to moving to England before next week's transfer deadline.