"He keeps telling me, 'You will be the next one. You will be the next one,'" Zambrano said.
Pappas was the most recent Cubs pitcher to throw a no-hitter, 36 years ago, until Sunday night. That's when Zambrano put his name next to Pappas' in the history books with the franchise's ninth no-no since 1900. Pappas knew Zambrano would eventually do it. He'd been calling it for the past six years.
"Finally, it's done," Zambrano said.
Now, Pappas has four months to think up a new phrase before the next convention. As for Zambrano, he celebrated the feat with a dozen friends and family members in his hotel suite. They had a quiet celebration, ordering room service and sharing a few bottles of champagne.
"I don't like to go out and show off, drink two or three glasses of wine and be a little dizzy," Zambrano said before Monday's game with the Astros at Miller Park. "Then people start looking at me. That's why I don't go out."
His phone battery was dead after the game. Once Zambrano got it charged in the hotel room, he found 50 text messages. Then, the Hall of Fame came calling. They'll get his hat and one of the game balls, but not the one he struck out Darin Erstad with for the final out.
"I was the one who threw the no-hitter, you know, not MLB, I have to keep something," Zambrano said. "My brother already asked for my undershirt. I know that there are some people, good friends or my dad might ask for something."
Zambrano said he'll remember the postgame celebration with his teammates most of all.
"When I was coming in, the players were side by side, like I was getting married," he said. "I was walking in the middle of my teammates, celebrating with me, a special moment, like a reception line."
Television stations in his native Venezuela cut to the game in the eighth inning, said Cubs shortstop Ronny Cedeno, who grew up playing ball with Zambrano's little brother back home.
"I think it's got to be crazy in Venezuela," Cedeno said.
Cubs manager Lou Piniella has been a part of a handful of no-hitters, mostly as a manager. He knew early on that Zambrano had his best stuff going, but he still held reservations. After all, Big Z hadn't pitched since Sept. 2 because of shoulder soreness, and he hadn't gone more than six innings in five of his previous six starts.
"My concern was the pitch count," Piniella said. "My other concern was how long he could carry that stuff into the ballgame, because he hadn't pitched in a while. He answered all those questions. From the sixth inning, seventh inning on, you knew he had no-hit stuff. It was just a question of whether they got a base hit or not."
Nick Zaccardi is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.