Allegri was hired last week to replace Sergio Conukicao, after he won the Scudetto in his previous time that was in charge.
Former Champions League and Brazil World Cup winner Cafu told La Gazzetta Dello Sport: “Allegri can bring the right grit, because Milan has always been a power in world football, but Allegri can offer the team a different spirit.
“I hope that (Gian Piero) Gasperini can do well, but there is a lot of pressure at Roma, it is a passionate place to work.”
With Real Madrid veteran Luka Modric to join Milan after the World Cup of Club, was Cafu Bullish.
He added: “I think it is an investment that could pay off. He can also bring a calm in the dressing room, even if he will clearly not be able to play every game.”