Seven years later, the Hockey Hall of Famer is proving to be prophetic.
Perreault, who played 17 seasons for the Buffalo Sabres, remembers how Eichel's dynamic skill set caught his attention at the 2013 World Under-17 Hockey Challenge in his hometown of Victoriaville, Quebec.
"From the first time I saw him, I immediately told myself: 'This guy is going to be a superstar in the NHL one day,'" the 69-year-old told NHL.com from Victoriaville this week. "I was so impressed with his skating, his shooting, the way he made plays.
"And now, that's exactly what he is -- an NHL superstar."
Video: Relive Jack Eichel's incredible 17-game point streak
Eichel fell a game short of matching Perreault's Sabres-record point streak of 18 games, from 1971-72, when he missed Buffalo's 6-1 loss to the Philadelphia Flyers on Thursday because of an upper-body injury. He returned to the lineup Saturday and had an assist when the Sabres defeated the Los Angeles Kings 3-2 to extend his personal point streak to 18 games.
"I think you've got a lot of confidence right now -- I'm the benefactor of some really good hockey," Eichel said. "It's a full team effort here and just trying to contribute, work hard."
Eichel has 51 points (24 goals, 27 assists) in 36 games. He's on pace to surpass his career highs in goals (28) and points (82) set last season.
"No one should be surprised that he's taken the next step this year," Perreault said. "He's only 23. He's only getting started."
Perreault, the Sabres leader in goals (512), assists (814) and points (1,326), said it's all part of Eichel's evolution on his continuing path to greatness.
"It takes time," Perreault said. "I came into the League in 1970 and it was a while until our Sabres team made the Final in 1975. It takes four or five years. A lot of it has to do with the guys around him. They've done a nice job surrounding him with talent, guys like [Jeff] Skinner, [Rasmus] Dahlin and [Sam] Reinhart. They're starting to jell and it shows."
"I won't be surprised if he breaks all the records in Buffalo if he plays his whole career there," Perreault said. "He's going to get all the records there if he's not hurt."
Video: BUF@NYI: Eichel scores PPG to tie it late in the 3rd
It's a crisp late November day in Buffalo and the Sabres are holding what is turning out to be an especially feisty practice drill at KeyBank Center.
For 10 seconds Eichel is in the corner trying to dig the puck out against three defenders. In this chaotic sea of sticks and elbows, he finally emerges with it and lets out a loud whoop to let everyone know.
"That's Jack," Sabres assistant Don Granato said. "He's just an ultra-competitive guy, even in practice. He's been that way since he's been 16. Before all of this hype at this level, he was every bit the competitor then. He's just more knowledgeable now, more experienced. And that's why the way he's playing now shouldn't be a surprise."
Granato would know. He was Eichel's coach with the National Team Development Program in 2013-14. Like Perreault, Granato knew there was something about the kid that might lead to future greatness from the moment he first saw him.
"I met him at our training camp in 2013 and you could see Jack was special right then," Granato said. "You could see he wanted to be impactful. When we stepped on the ice, results mattered. Winning matters. Then. And now. You could see that.
"Look at our practice. We run any drill and you can see he wants to win it. He's a leader. Always has been."
Granato points to the 2015 IIHF World Junior Championship as an example. He was an assistant with the U.S. team when a group of older players approached the coaching staff calling for Eichel to be captain.
"We thought he was too young for that," Granato said. "He was only 18. But they convinced us. It says a lot when your peers, even the older ones, respect you like that and want to be around you.
"That's why I don't think it's fair when people look at how he's playing this season and say 'Well, he's just matured.' He's always been that way. He's continuously made himself a better player. He's at a point where he's been through the League enough where he's got that pure confidence in his ability to play and lead."
Video: BUF@FLA: Eichel dekes defender, buries wrister
Toronto Maple Leafs center Auston Matthews, Eichel's teammate with the U.S in 2015, has seen firsthand how much the Sabres forward has elevated his game. In the past three weeks, Eichel had eight points (three goals, five assists) in three games against Toronto.
"He's been on fire, he's extremely confident to begin with but when you're really feeling it like that, every time you touch the puck you feel dangerous and that the puck is going to go in," Matthews said. "He's been at the forefront of that."
Opponents also are noticing Eichel's improvement in his own end. He entered the season as a career minus-65 player; this season he is plus-16.
"As you go through ups and downs and try to find ways to get better, you realize how important playing away from the puck is," Toronto captain John Tavares said. "He's certainly getting better … he's one of the best players in the League."
Eichel and Granato were walking to the team bus after Buffalo's 5-3 loss to the Maple Leafs at Scotiabank Arena on Tuesday when a fan yelled a message at him.
"Jack, you're going to win the Hart Trophy!" the supporter said.
Eichel didn't hear him. He was listening to music on his headphones. Even if he had, the topic of the Hart Trophy as NHL MVP isn't a subject he wants to hear about.
"We've got a long year here," he said. "Not even halfway through the season. I'm not thinking about it at all. There's a lot our group needs to accomplish. A long way to go for us to be where we want to be coming into the Playoffs."
Eichel's reluctance to talk about the MVP race hasn't stopped the outside conversation from putting him among the leading candidates with centers Nathan MacKinnon of the Colorado Avalanche and Connor McDavid of the Edmonton Oilers. Eichel said he studies the nuances of MacKinnon's game.
"The discrepancy between the best player and the bottom line ... it's not crazy," Eichel said. "The little details really add up. I think all the best players do it, and I'm just trying to do it myself."
Video: TOR@BUF: Eichel pots wrist shot on odd-man rush
It's something that has been noticeable according to forward Sam Reinhart, Eichel's teammate with the Sabres for five seasons.
"There's just a different strength in everything he's doing," Reinhart said. "Strength, power, composure, you name it. I could have told you this was going to happen with him. You could see it [progressing].
"We've always known the dominant force he could be, and he's had a tremendous amount of success. But I think it's a combination of he's coming into his own and how our team is playing too."
Eichel is showing the hockey world this season what he's always been capable of. To that end, just how high can keep elevating his game?
For Buffalo coach Ralph Krueger, it will be fun to see what the answer is.
"Is he one of the best players in the League? He always has been for me since Game 1," Krueger said.
"Let everybody else decide [Hart favorites] right now."