The Rossoneri want the World Cup winner to accept a position with their Allievi Nazionali side, but the 38-year-old is sorely tempted to postpone his plan to hang up his boots
The striker's contract with the club will expire at the end of June but the Rossoneri have offered their 2007 Champions League final hero a job with their Allievi Nazionali side.
Inzaghi has explained that while he felt he would want to retire following his dream San Siro send-off against Novara last month, when he netted the winning goal in a 2-1 win, he is now having second thoughts.
"I have not decided my future," the former Italy international told the club's official website.
"I thought after Novara that a small light would go off in my head to make me quit, but has not yet turned on.
"It's quite a dilemma. I am at a crossroads and is difficult to decide. I'm flattered by the offer to coach the youngsters, but my heart is telling me to play again.
"I still really want to take to the field. But I'm going on vacation and then I'll decide."
Inzaghi joined Milan in 2001 and has scored 73 goals in 202 Serie A appearances for the club.