With the Premier League transfer deadline having passed, the options for the centre-back must now come from the rest of Europe, but he still seems to have plenty of suitors for his services.
Sources have confirmed to Goal that Monaco have started asking about Rugani's availability, though negotiations of an actual deal have yet to take place between the two sides.
The centre-back would address a need for either Roma or Monaco, with the Serie A side having shipped 48 goals in 38 league matches last season while finishing sixth.
Monaco’s record at the back was far worse as the club struggled through a terrible season in Ligue 1, letting in 58 goals and finishing just above the relegation zone.
Rugani's place with Juventus is up in the air at the moment, with the club boasting Giorgio Chiellini and Leonardo Bonucci as first-choice centre-backs.
The club also landed Merih Demiral from Sassulo and Ajax star Matthijs de Ligt this summer, likely leaving him as part of a third-choice lineup.
The defender played just 15 times in Serie A last season, down from 22 the year before, as Juventus cruised to another league title, and could see his minutes fall even more drastically this term.
Despite that, he seems content to stay with the Turin side should a move not get done.
New Juventus boss Maurizio Sarri and Rugani have a good relationship from their time together with Empoli, where Rugani was named to the Serie A team of the year.
Juventus get their title defence under way on August 24 against Parma in what will be Sarri’s first official test as boss.
The club will then face last year’s runners-up, Napoli, in their second match of the Serie A season on August 31.