The 40-year-old, who spent the last decade of his playing career at San Siro, is expected to replace Clarence Seedorf, who looks set to be sacked.
Inzaghi, in charge of the club's Primavera team, would happily continue coaching the Under-19s if nothing came of the reports.
"Excited by what I'm reading? Who doesn't get emotional about what they read? Milan is my life and my story," he told the Milan Channel.
"I've stopped playing for Milan but I do everything they ask of me. We'll see what happens, I'm a Milan employee until 2016.
"I could have left but I wanted to stay because I have a contract here. That's the path I will follow.
"If some good news is communicated to me then great. Otherwise, I am proud to continue coaching these boys."
Inzaghi, though, insists that he has heard nothing beyond the media speculation surrounding his future.
"I have had no other communications about it until now, other than what has been written," he said.
"I am a Milan employee. Of course, if Milan call and ask me to fulfil another role I will be very happy, but if not I will remain to coach the Primavera as I have always done.
"If there is no further communication I will preside over the Dossena Tournament, where we will be present. That is what we are preparing for."
