Allegri spent almost four years in charge of Milan before leaving the club midway through last season after a poor run of form.
However, he was appointed as Antonio Conte's successor in July and will be tasked with helping deliver a fourth consecutive Serie A title.
Both Juve and Milan have taken maximum points from their opening two league games in 2014-15 and Allegri is expecting a special atmosphere for the fixture.
"I spent three and a half wonderful years [at Milan] and it goes without saying that I always had a great relationship with [chief executive Adriano] Galliani, the president and everyone else associated with Milan," Allegri said on Friday.
"It'll be a special and emotionally-charged evening. Milan made some good quality signings during the transfer market, including [Fernando] Torres and [Giacomo] Bonaventura who are technically gifted and above all in terms of their mentality."
While this season has represented a new challenge for Allegri, it is much the same for Filippo Inzaghi - who has made a solid start to life in charge at San Siro.
The former Milan great will hope to improve on the club's eighth-place finish last time out and Allegri feels that will prove the motivation for Saturday's hosts.
"Inzaghi has done well to breathe new life into a club which has had a difficult six months or so," he added.
"We have to prepare ourselves for a rejuvenated squad who, other than possessing quality, will want to show they can fight for the top three places in the league.
"Tomorrow will be an important game for them."
Arturo Vidal could return for Juve after a knee problem, although Andrea Pirlo remains a week or so away from fully shaking off a hamstring injury.
