Allegri left Milan at the end of last season and took over at Juventus, while former Italy striker Inzaghi swapped the iconic black-and-white stripes for the red-and-black Milan jersey in a high-profile transfer in 2001.
Since replacing Allegri, Inzaghi has guided Milan to a 3-1 win at home to Lazio and a thrilling 5-4 success at Parma that included Jeremy Menez's sensational backheel goal and another sterling performance from Japan attacker Keisuke Honda.
"He reminds me of a young [Louis] van Gaal," said Milan midfielder Nigel de Jong of Inzaghi before the Dutchman rued the presence on the in-form Carlos Tevez in the Juventus attack.
"If I could take one player out of the Juve team it would be Tevez. Carlitos is a true warrior. He is a crucial piece of the current Juventus."
The magnitude of this weekend's game at San Siro is not lost on De Jong, who added: "It's certainly our first real test, but it's also Juve's."
Juventus have also begun the season impressively as they seek a fourth successive Serie A title and Allegri hopes to have influential midfielder Arturo Vidal back from injury against Milan.
"Against Juventus we will need to play a perfect game," said Inzaghi.
"We have nothing to lose because they are a stronger team, but in football you never know. I hope that the San Siro and our fans can help us achieve a miracle."
Inter, for whom 21-year-old striker Mauro Icardi bagged a hat-trick in last weekend’s 7-0 thrashing of Sassuolo, are at Palermo on Sunday, while fellow title contenders Roma are at home to Cagliari.
Sampdoria, in fifth, will hope for more magic from Stefano Okaka when they visit Sassuolo, who must content without suspended talisman Domenico Berardi.
Atalanta and Verona, who are level with Inter and Sampdoria on four points, are at home to Fiorentina and away to Torino respectively.
Fiorentina striker Mario Gomez sat out much of last season through injury and has missed some gilt-edged chances so far this term.
"They have not seen the real Mario Gomez," he stressed. "When I don't score for two or three games, everyone is talking about me.
"I'm not worried. I want to score as soon as possible and I am certain it'll happen."
Udinese host Napoli in a game between teams on three points apiece as Genoa entertain Lazio.
Empoli and Parma, the only two sides without a point after the opening two games, will hope to get off the mark away to Cesena and Chievo respectively.