The 25-year-old centre-back has made only three competitive appearances for Juve this season and dropped to the bottom of the pecking order, behind Merih Demiral.
With Giorgio Chiellini expected back in training at the end of this month after ACL surgery, it gives Rugani even less chance of playing time in Turin.
According to Sky Sport Italia, Calciomercato.com and more, Leicester City are the favourites to snap up the Italy international for €20-25m.
There could even be a loan deal with option to buy at the end of the season.