Inzaghi took over the reins at San Siro in the close-season, replacing former team-mate Clarence Seedorf, who had in turn succeeded Allegri at the helm.
Now head coach of defending Serie A champions Juve, Allegri returns to his former employers on Saturday with both sides boasting a 100 per cent record after two matches this season.
Quizzed on his relationship with his opposite number, Inzaghi dismissed any talk of a rift between the pair, despite some disagreements in the past when he played under Allegri at Milan during the latter stages of his career.
"I had some misunderstandings with Allegri but they have been cleared up," he said.
"Let’s look forward and enjoy this match with the stadium full of our fans. I am very happy. From every coach that has coached me I have learnt something.
"Allegri is a very prepared coach and he will make our lives difficult.
"He has a great team and I wish him all the very best, but after [Saturday's] match!"
New signing Fernando Torres is yet to make his Milan debut since arriving from Chelsea, the Spaniard having sat out the incredible 5-4 victory over Parma last weekend through injury.
"Torres tried to recover to be on the bench," Inzaghi said. "We didn't risk him, but I've noted him charged just like [Stephan] El Shaarawy.
"We'll see if they will be available to play from the start. I will make my assessments for the starting XI.
"I am spoilt for choice in all areas. I will evaluate match by match the best players and the options to use from the bench.
"I will evaluate with my staff the right solution to take on the Juventus defenders. It's better to be in large numbers during these occasions because you take on the matches calmer and aware of the strength of your substitutes."