Wanyama discussed De Zerbi when announcing his retirement on Friday.
The Kenyan great said, "I have studied him closely. Everywhere he has gone, he has improved teams.
"I've long admired De Zerbi since I noticed what he was doing with Sassuolo. Look at Shakhtar, Brighton and Marseille. He changes sides, he moulds them so they're not just survivors, they're competitors.
"I firmly believe he is the right man for Tottenham. He can keep them up, 100%.
"He may need to compromise principles at first, but he is very experienced; he knows what is missing and what is necessary."
On Tottenham's future, Wanyama is optimistic: "It's been difficult for the coaches at Tottenham this season because of the amount of injuries they have had. They have had 10 to 15 players out at different times, and that certainly didn't help.
"The club has tried different approaches but it's tough when you don't have all the squad back together.
"If they can get Kudus, Maddison and Bentancur back, they can play a big part in turning it around. Also getting Solanke back into a rhythm. It will make them much more solid as a unit when they have that threat."