It was announced last week Allegri will step down at the end of the season following a five-year spell in which he has led Juve to five Serie A titles:
Pochettino has emerged as one of the leading candidates to replace him, and Daniele Pochettino told Tutto Juve (h/t MailOnline's Jeorge Bird) it is possible his cousin could make the switch to Turin after leading Spurs to the 2018-19 UEFA Champions League final:
"In my opinion [Pochettino replacing Allegri] could be feasible, because Mauricio is a coach who has shown he knows how to work well, and reaching the final with Tottenham is a clear example. If he plays it like he does all games, for me it's the right year to win. I met him a few months ago, I met a very nice and helpful person.
"The Bianconeri's goal is, of course, the Champions League, and my cousin has all the useful qualities to be able to coach this club. Mauricio showed he had the right experience to be able to coach in Europe. With Tottenham he was able to forge a group of individuals that was not so well known.
"Everyone in the family would like to see him at Juventus.
"He is certainly attracted to Italy, he told us he would like to come here to find his ancestors. We also talked about Piedmontese cuisine, which he would like to try again."
Marcello Lippi, also a five-time Serie A-winning coach with Juve in two separate spells, has similarly talked up the idea of Pochettino taking over from Allegri.
He has hinted that Juventus may be waiting for this season's all-English European finals to be over to appoint a new boss.
Sarri is another manager who has been widely linked with Juve since the Allegri announcement:
Arjun Pradeep @IndianRegista
🇮🇹 📰 | Front pages of Gazzetta & Corsport headline that Maurizio Sarri is the favourite to become the Coach of Juventus. Juve are moving forward on him & have already contacted him. They're now waiting until after the UEL final. But the Pochettino track is still alive as well. https://t.co/m7n3ihXMsO
And, per Sacha Pisani of Goal, Lippi believes Juventus may be waiting for the Italian or Pochettino to get their respective seasons out the way:
"Why hasn't a well-run club like Juventus named the successor to Allegri yet? Well it's a difficult decision to make, but perhaps they are waiting for a certain competition to end. We'll see if their new coach comes from those involved in either of the all English Finals, then we will understand the reason for the delay of the announcement.
"This year the English clubs are the best in Europe, but these things go in cycles. I think Sarri has a great chance at winning the Europa League, then there is Pochettino whose family is from Piedmont."
Sarri, 60, has only been at Chelsea since last summer, when he joined from Napoli, and despite receiving widespread criticism from the club's fans, he could finish the season with a top-four Premier League finish and a European trophy.
According to Sky Italia (h/t Calciomercato), Chelsea legend and Derby County manager Frank Lampard is being lined up as Sarri's successor should he get the Juve job, while the Old Lady have also been in contact with Simone Inzaghi over replacing Allegri.
It is no surprise that some of Europe's best managers are being linked with Juve given they are one of the biggest clubs in the world.
Argentinian Pochettino would be a rare non-Italian Juventus manager, coming over a decade after their last, Frenchman Didier Deschamps.
But he is arguably the most exciting candidate linked to the Italian champions, and if he wins the Champions League with Tottenham, he will finally have a major piece of silverware to show for his remarkable work in north London.