Pulisic struck twice in victory over RB Salzburg this week.
But the American is determined not to be compared to his predecessor Hazard, now of Real Madrid.
“It's what I'm out there to do," he said. “I'm in an attacking position. I want to score goals, I want to help them with assists and do a lot of good things. My work defensively is important too.
“I'm not trying to fill (Hazard's) gap, he was an unbelievable player. I want to be my own player, to look at me like that, do the best I can and perform the best I can for the team.
“It's pre-season now and I still have my opportunity to prove when the real season comes around."