Allegri won the Scudetto with Milan in his previous time who was in charge.
And he has now been re -appointed by Milan after more than 11 years away.
Dida told Sky Italia: “I see him well. After last season it was necessary to change and start again with a coach who knows the environment in which he has already won.
“In my opinion, he can strive to return to the Champions League and win the Scudetto.”
On Gattuso as a coach of Italy, Dida said about his former teammate of Milan: “I am happy for him because he is a friend of mine. He has grown a lot as a coach and now he has a great opportunity.
“He will bring a lot of determination and the Italian national team has a person as he needs. I wish him the very best and I hope he can lead Italy to the World Cup.”