Gattuso has been linked with Max Allegri's job at Milan.
But Andrea D'Amico insisted: "He's a player first, his contribution is in the locker room and has always had a great love for his work. He has made a commitment, is finally back at his best levels.
"The Milan bench is a suggestion only in the media, no one has ever offered anything and it all starts with what he did in his career with the Rossoneri. There are absolutely no assumptions.
"I already told him: when the club decide to sack Allegri, its Pep Guardiola who already has it and it is Tassotti who knows all the environment."