The 19-year-old Australian provided one of the biggest shocks in Wimbledon history with a four-set win over Nadal, becoming the first player from outside the top 100 to beat the world number one for 22 years.
The triumph put the wildcard entry into the quarter-finals at SW19, and McEnroe believes that he could go on to emulate Boris Becker, who won the tournament three times between the ages of 17 and 21.
"We've been waiting for this for a while. We keep saying, 'Who's the next guy?', and I think we found that guy right now. I've been hearing about this guy for years. I'd only seen him play a little bit," McEnroe told BBC Sport.
"But that was absolutely stunning, to see what he did to the world number one. How did he keep that up? This is where it gets a little tricky. But he actually had this feeling about him. I could see it from the commentators' box, that he absolutely believed he was going to win this match, and he's acting to me like he can win this tournament.
"The last guy I saw like this is... Boris Becker, that young teenager, no fear whatsoever - 'no matter what comes my way I'm going to be better than them.'"
Kyrgios, who is currently ranked as the world number 144 but will climb into the top 100 courtesy of his exploits at Wimbledon, will face Milos Raonic in the last eight.