The World Cup and European Championship winner took over as Les Bleus boss from Raymond Domenech in 2012 after spells in charge of Marseille and Juventus and the former AC Milan midfielder is not surprised that things have gone well for him.
"I had the honour to play against Didier Deschamps, he is one of my idols," Gattuso told RMC Sport.
"What I see now [Deschamps as France coach] I'm not surprised by. He is a man of football. He succeeded because he always had a great passion for football. He was already a coach when he was on the pitch."
The former Italy international also remembered playing against France legend Zinedine Zidane, recalling that the thought of playing the one-time Ballon d'Or (then the European Footballer of The Year) winner gave him sleepless nights.
"Every time we had to play France, it was me that had to mark Zidane," the midfielder continued. "The night before a game, I did not sleep. I said prayers because I knew he was going to do magic.
"In the end, it was always me who had to look like a fool when I found myself facing Zidane."
Gattuso left Milan in the summer and now plays for Sion in Switzerland.