The veteran striker leaves San Siro this summer after an 11-year spell with the club and Inzaghi insists he will not forget the Rossoneri easily.
"Milan will always remain in my life and in my heart," Inzaghi was quoted as saying by La Repubblica.
"I hope that Milan will be a part of my future, not as a player but hopefully as a director. If I don’t return to Milan soon, then I will return later because Milan have given me everything."
Inzaghi then went on to discuss his immediate future, and stressed that he's still undecided as to whether he will hang up his boots or continue playing.
"I know that there are clubs interested in me, but it’s a difficult choice. On one hand it would have been right to end my career with a goal, but on the other hand I still have the desire to play and I feel well.
"I still have a lot of passion to play football and score goals. To give up playing football annoys me a bit, that’s why I’m still thinking about my future."
The 38-year-old has recently been linked with a move to Fiorentina.