The Milan boss has suggested that he would be interested in taking charge of the national team if Cesare Prandelli leaves his post, and Gattuso thinks he has all the attributes to succeed at international level.
Prandelli has hinted that he could leave the national side after the 2014 FIFA World Cup, and Allegri has already been linked with the role.
Gattuso - who worked under Allegri at Milan for two seasons - has seen enough to convince him that he would be the ideal candidate for the role.
"Allegri has the capability to do well," he told Sky Sport Italia. "Leading Italy is a great responsibility, but Max has shown that he is a very good tactician. He would do well if given the role."
The 35-year-old Palermo boss also refused to rule himself out of the running for the job, but insisted next year may come a little bit too early for him.
"For now I’m focused on taking Palermo into the top flight," he added.
"Saying that, I, like Allegri, am targeting such a role but I have a long road to go down first. I could think about it one day though.
"I was in the Azzurri (national team) for 11 years, I know what a happy Azzurri dressing room is and I’d like to breathe that air again."
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