Seedorf's future as Milan head coach remains shrouded in doubt, and Inzaghi is viewed as the most likely successor should the Dutchman depart San Siro.
Gattuso was a team-mate of both Seedorf and Inzaghi at Milan during his playing career, and urged the Italian giants to allow Inzaghi time if he is appointed.
Speaking to Gazzetta dello Sport, he said: "Filippo Inzaghi has always been destined (to be a coach).
"For many of us when he played he seemed an athlete of pure instinct, but behind that was work.
"There has always been an intense phase of study. He knew his opponents better than anyone else.
"It was natural that he has arrived as coach of the first team, but Inzaghi is a young coach and must be protected."
Milan endured a difficult campaign last season, eventually limping to an eighth-place finish in Serie A.
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