Italian website Transfer Market Web is reporting that the Gunners are keeping tabs on the 23-year-old centre-half as Arsene Wenger looks to make defensive reinforcements ahead of the new season.
According to the story, the north London side were interested in the Italy international last summer but a move failed to materialise as Arsenal signed Germany international Shkodran Mustafi.
However, the same article states that the Serie A champions are unlikely to entertain the prospect of Rugani leaving Turin in the current transfer window.
Rugani scored two goals in 15 appearances in the Italian top flight last season as he provided back-up for Giorgio Chiellini, Andrea Barzagli and Leonardo Bonucci.
However, the latter defender has since completed a controversial move to their Serie A rivals Juventus to leave manager Massimiliano Allegri missing a key component of his back three.
Arsenal signed Bosnian defender Sead Kolasinac in a free transfer from Bundesliga outfit Schalke 04 in the summer transfer window.
The Gunners boss have also added France striker Alexandre Lacazette to their squad in a club-record £52m deal from Ligue 1 side Lyon.
Arsenal will start their Premier League campaign with a home clash against Leicester City on Friday night.
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