Inzaghi succeeds the sacked Clarence Seedorf.
"Inzaghi will ensure Milan's history is respected," Gattuso said. "He will make it understood that technical and physical qualities are not enough and that behaviour matters too.
"I don't deny that I am happy for Inzaghi, he has always shown his attachment to the Milan shirt.
"Me on the Rossonero bench? I would be a hypocrite if I denied that I would like to return to Milan one day."
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