The British tennis player has made superb progress over the past 12 months to climb into the top five of the world rankings and the American great thinks he has all the attributes to win several major titles.
Speaking after Draper's four-set win over home favourite Gael Monfils at the French Open on Thursday (29.05.25), McEnroe told TNT Sports: "I tell you one thing, he won a lot of fans tonight with the way he played and the way he acted and the way he handled the whole situation.
"It's one of those matches that you’re proud to be a tennis player. You look back at these two guys digging that deep, you're looking at a guy 38 years old that is still moving unbelievably well, and you see Jack Draper maturing, playing better and better on the spot.
"I mean, I'll be surprised if he doesn't win multiple majors. It is incredible how much he's improving and how great a player he's become."
The seven-time Grand Slam winner continued: "He can do everything.
"He's an excellent volleyer, the serve is huge. He took his shirt off and I was immediately jealous. The guy is in unbelievable shape.
"I tell you, he's got a lot of big things to look forward to."
Draper will now face highly-rated Brazilian youngster Joao Fonseca in the third round in Paris and McEnroe thinks the clash could be a blockbuster.
He said of Fonseca: "He's absolutely going to bring the flare, he's also going to bring a lot of fans with him so it'll be interesting to see where they put that match.
"It might be a little bit annoying for Jack to have the crowd against him again but I think that's what's going to happen, especially if it's on a rather small court, so he's going to have to rebound quickly.
"I doubt that will be a night match, but it certainly could be because that's box office for us.
"You're going to see a lot of those two in the next 10 years."