"He can be one of the best in the future for sure," he told The Associated Press.
Hazard thinks Pulisic can follow in his footsteps.
"He can be (a star)," he said. "Now he's at one of the best clubs in the world," he said.
"He's a proper player," Hazard continued. "He can play football."
Hazard made his long-awaited move to Real Madrid this summer after months of indication that his days at Chelsea were numbered.
Now that he's at the Bernabéu, he's tasked with leading a team that is coming off one of its worst seasons in club history, one in which Madrid didn't come close to winning any major trophy.
It is Madrid's first major signing since Ronaldo left for Juventus last summer. The move for Hazard cost Real about $113 million. There is pressure on the 28-year-old Belgian to win fast.
Hazard's first victory of the summer in a Real Madrid jersey, however, was off the field. He will be the coverman for EA Sports' FIFA 20 video game.
"When you play football, it's a dream to, first, be in FIFA and then to be on the cover," Hazard said.
"You want to play more often because you're on the cover," he added.
Hazard has more than that on his mind right now, though. He joins manager Zinedine Zidane, Hazard's childhood idol, in their attempt to restore Madrid's esteemed name.
Hazard also joins 2018 Ballon d'Or winner Luka Modric and striker Karim Benzema in their endeavor to net the goals that haven't come in Ronaldo's absence.
Hazard's game has always been predicated on his elusiveness and passing ability — not his scoring. Though he was Chelsea's leading goal scorer each of the past two seasons, his instincts have always told him to develop for his teammates. He doesn't plan on altering that in Spain.
"I'm not going to change anything. That's why I'm here," Hazard said.
Hazard comes to Madrid with rudimentary Spanish-speaking skills. Real winger Gareth Bale — who also joined Real from the Premier League for a transfer fee of over $100 million — has been roundly criticized despite his success over the years for his aloofness with teammates due in part to his limited Spanish-language abilities.
"At the moment, I'm not learning. But for sure when we go back to Madrid, I need to take some lessons because my Spanish is not — I can understand. That's the good thing," Hazard said. "But to talk is hard. You try, you try, you try. One year, I'm going to talk Spanish."
Zidane said Sunday "let's hope, for everyone's sake" that Bale is transferred to another club.
Hazard is in the United States for a series of exhibitions Real has scheduled, including one against rival Atletico Madrid tonight in East Rutherford, New Jersey.
Hazard enjoys New York, as he does Los Angeles and Washington. He likes American culture. But, when informed that many American kids play FIFA, but don't necessarily follow professional soccer, his eyebrows furrowed.
"They will for sure. Because of me on the cover, first, and then they will see me, and then they will watch soccer," Hazard said with a smile.
An aspect of American culture that Hazard reveres is basketball. He's a New York Knicks fan. But, in light of their offseason, Hazard says with a laugh that "it's better we don't talk about it."
Like Steph Curry, the Warriors' two-time MVP, Hazard has a younger brother, Thorgan, who plays the same sport. Thorgan Hazard transferred to Borussia Dortmund this summer (Pulisic's old club). Seth Curry signed a four-year, $32 million deal with the Dallas Mavericks this month.
"I'm Steph Curry," Hazard said when asked whether he was more Steph or Seth. "I'm the best one."
Previously, Hazard said that he "doubts" he would ever play in MLS. On Thursday, he hedged those bets.
"In football, you never know," he said. "I'd like to say that in the future I'd like to play there, there, and there. Of course, at the moment, I'm in Madrid, so I don't know."
After Friday's friendly in New Jersey, Real has three more exhibitions before its league opener at Celta Vigo on Aug. 17. Hazard can't wait. He's eager to finally play his first official game in a Real uniform.
"Friendly game is OK, but I want to play La Liga," Hazard said. "I want to play Champions League. I want to play in the Bernabéu as well."
And he's got a few butterflies to boot.
"Of course, of course," he said. "Always. When it's a new season, it's always like that."