Seedorf is widely expected to be relieved of his duties after just four months in charge of the San Siro side, and 40-year-old Inzaghi has been lined up to take his place ahead of the 2014-15 campaign.
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And the former Rossoneri striker, who currently caches the club's Under-19 side, says he will follow the clubs wishes regarding any future coaching role.
"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 the Primavera team."
However, Inzaghi 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 continued.
"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."
Seedorf replaced Massimiliano Allegri as Milan coach in January, but the club failed to qualify for European football for the first time in 16 years.