Inzaghi, who enjoyed an 11-year spell as a player Milan, became the club's head coach in June, replacing his former team-mate Clarence Seedorf.
The 41-year-old may have only been in charge for five months, but he is already setting his sights on the long term.
Inzaghi has stated his ambition to match the longevity of Ferguson, who enjoyed a trophy-laden 27-year tenure at United before retiring in May 2013.
"The last time the president was at Milanello, he said he would like me to be the coach for the next two decades," he told Corriere dello Sport.
"Therefore I say that my dream is to become the [Alex] Ferguson of Milan, because this shirt has given me everything, this club understands me.
"The President always wants to excel, he wants to win again, that's clear. They all want me to do well, and I know that they'll support me, even in difficult times."
Inzaghi has also backed misfiring striker Fernando Torres to prove his goalscoring credentials at Milan.
Torres has scored just once in nine Serie A appearances since joining Milan on loan from Chelsea in August.
But Inzaghi is confident the Spaniard will soon find his form and likened his situation to former Milan striker Hernan Crespo, who initially struggled at San Siro under the stewardship of Carlo Ancelotti.
"So far a lot of players have scored goals, just not the strikers, apart from [Keisuke] Honda," he added.
"Goals from Torres and [Giampaolo] Pazzini will come.
"I hope Torres will be like Crespo under Ancelotti, who for months didn't score , then he broke his duck and became Crespo.
"So far Torres has been struggling with an ankle injury, but now it's better and I thought he played very well in Genoa [in last Saturday's 2-2 draw at Sampdoria]."
