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."
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."
