According to Rai Sport (h/t Calciomercato's Kaustubh Pandey), Juve are considering their options after selling Leonardo Bonucci in the summer, with loan signing Benedikt Howedes having been restricted to just one appearance all season due to injury problems.
Mustafi is the man they have identified to help them ahead of the January transfer window.
The German had a match to forget in Arsenal's 3-1 defeat to Manchester United last Saturday. He dithered on the ball to allow United to take a 2-0 lead after just 11 minutes, per James Olley of the Evening Standard:
James Olley @JamesOlley
#afc 0-2 #mufc What a move. Arsenal (Mustafi) lose it badly again but its a great counter-attack with Lukaku and Martial combining before Lingard finishes in off Cech's left-hand post.2017-12-2 17:41:51
Mustafi subsequently went off injured, though Bleacher Report's James McNicholas offered a different diagnosis:
Mustafi going off with what looks like a broken spirit.2017-12-2 17:42:50
The centre-back had been enjoying some excellent form for the Gunners prior to that, though. Per Sky Sports News, he was one of seven nominees for the division's player of the month award for November.
Goal's Chris Wheatley shared his numbers after he helped Arsenal beat Huddersfield Town 5-0 in the final match of the month:
Chris Wheatley @ChrisWheatley_
Shkodran Mustafi vs. Huddersfield https://t.co/4YYXKoscjY2017-11-29 22:09:50
That's the kind of performance Juventus would want to see from him week in, week out as they seek to win their seventh Serie A title in a row.
The Bianconeri have also made the UEFA Champions League final in two of the last three seasons and will be hoping to compete in the latter stages of the competition again this year, though Mustafi is yet to experience that with Arsenal.
Aside from some errors along the way, such as the one against United, Mustafi is a strong choice at centre-back and has shown his value to Arsenal, per WhoScored.com:
Stoke are the only team to have scored vs Arsenal in Shkodran Mustafi's last 9 Premier League appearances. In 50 PL games since he signed, Arsenal's goal difference is +35 from the 32 he has started and just +4 from the 18 he has missed. Underrated? https://t.co/I9hJydnTDc https://t.co/kerOoJsli72017-11-20 13:30:02
While some of the mistakes he's made and the occasional lapses in concentration hint that he is perhaps not quite a top-class operator, he could still be a solid acquisition for a club like Juventus.
Arsenal would likely be reluctant to part with him in the middle of the season, though, so his capture could be tricky to pull off.